#deflection and radius of curvature

[tutoroot]

What are the Characteristics of Convex and Concave Mirror? 

In Physics, students often encounter the term, spherical mirrors, while learning about how light is deflected and at what angles. Several concepts and chapters are directly derived from it. There are two types of spherical mirrors, Convex Mirrors and Concave Mirrors. 

Convex mirrors and concave mirrors differ in their principles. In simple terms, convex mirrors bulge outside whereas the concave mirror bulges from inside. 

Tapering figures represent convex mirrors while broadening ones refer to concave mirrors. 

While, both, convex and concave mirrors have different principles, the complexities and comparisons need to be dealt with elaborately. From plane to spherical mirrors, to concave to convex mirrors, the differences attach immense importance to physics students, as well we those who deal with as part of academics as well as profession. 

In this article, we are happy to take you through various aspects of convex mirrors and concave mirrors. We cover: 

Convex  mirror uses 

Concave mirror uses 

Convex mirror examples 

Concave mirror examples 

Characteristics of convex mirrors 

Characteristics of concave mirrors 

Convex mirror diagrams 

Concave mirror diagrams 

Through ray diagram, as well as formula, we will also help you understand the difference between concave mirror and convex mirror, more clearly 

What are Plane Mirror and Spherical Mirror? 

However, before we delve into types of convex mirrors and concave mirrors, let us first talk about the basics of Plane Mirrors and Spherical Mirrors, and how they are different from each other, as well as their applications. 

Plane Mirror 

A plane mirror is a mirror that has a flat and smooth surface, which in turn, always forms a virtual form of the object, with exact shape and size, when it reflects.  Commonly, plane mirrors are those which people generally use in dressing rooms or makeup tables. A plane mirror is known for providing exact image. 

A plane mirror is used for a wide range of applications and purposes that include periscopes and kaleidoscopes, auto industry, mirrors for domestic use, medical especially dental, and torch lights, besides security-related purposes. 

In terms of physics, when light rays hit a plain mirror, the angle of reflection will be the same as the angle of incidence. In plain mirrors, the images are generally laterally inverted, and are erect. The focal length of a plain mirror is counted as infinity. 

Spherical Mirror 

Spherical mirrors are also referred to as curved mirrors, where they have a shape cut out of the spherical surface. Under a spherical mirror, there are two categories: convex mirror and concave mirror. The spherical mirror and its equation hold significant importance in science, owing to its association with optics. 

Unlike plane mirrors, spherical mirrors, both convex mirrors and concave mirrors, have a radius if curvature with a consisting curve, which results in the formation of an image, that can be either virtual or real. 

What is a Concave Mirror? 

A Spherical Mirror that has a reflective surface inside, is called the converging mirror. The main attribute of the concave mirror is that it focuses on pointing the light from the source falling on it, into a single point. And generally, the image formed by these types of mirrors usually varies based on the size, shape, and position of the object. 

Characteristics of Concave Mirror 

The major characteristics of concave mirrors are listed below, 

Converging: A concave mirror is a converging one because, light rays that hit it reflect on the surface, and merge at a particular point. This point is known as a focal point. Concave mirrors allow light to focus to a point. 

Magnification and formation of image: Place a concave mirror close to any object and you will notice that it shows a magnified image that is straight, erect, and of course virtual. The image looks to be larger than the actual size of the object. The concave mirror also looks upright. The reason why concave mirrors feature the formation of virtual images is that the rays that reflect look to diverge from a point located behind the mirror. 

Distance and image properties: In concave mirrors, when the distance between the object and the concave mirror increases, the size of the image decreases. At a particular distance, , the image changes to virtual. Under this circumstance, the true image, in an inverted form manifests on the opposite side of the concave mirror. 

Image formations: concave mirrors create images of different sizes, and diverse in nature, from real to virtual. These features enhance the importance of concave mirrors, which they are widely used in various applications, from domestic to scientific 

Image Formation by Concave Mirror 

The image formed by the concave mirror is either real or virtual and can be small and large based on the position of the sources, and the reflecting point. 

For example, if the distance of the object from the source is large, then it results in real and inverted images. Whereas for the objects placed close to the source, the images formed are erect and virtual. 

Moreover, in this mirror, the light converges at a single point before reflecting, which is referred to as a converging mirror. 

Ray Diagram of Concave Mirror 

The Ray diagram of concave mirror is shown below along with the object placing. 

The object is at Kept at Infinity: When the parallel rays meet or converge at the Principal Focus, F. So when the object is kept at Infinity, the image will form here at the F. The image formed by this ray diagram is a point-sized, highly diminished, inverted, and real image. 

Object is placed at infinity and Centre of Curvature: Only diminished images are formed that are either real or inverted.Object at Centre of Curvature(C): The image of the same size is formed, that is inverted or real. 

Object between Principal Focus and Centre of Curvature  

Object at Principal Focus(F): A highly enlarged image, that is inverted and real.  

Object between Principal Focus(F) and Pole(P): Similarly enlarged is formed.  

It is the complete description of the ray diagram of concave mirror when the object was placed at various points. 

What is a Convex Mirror? 

Convex mirror is also a spherical mirror and is exactly opposite of concave mirrors in its properties. 

Let us first understand convex mirror through its basic definition: 

A convex mirror is a type of spherical mirror that has a reflective surface towards the outside of the bulge, and it is also referred to as diverging mirror. Unlike convex mirrors, in a concave mirror, the light falling on the object diverges as it reflects through the mirror. And generally, as the distance between the source and the object decreases, the size of the image formed increases. 

Characteristics of Convex Mirror 

Diverging: A convex mirror is a standard diverging mirror because when light rays hit the reflecting surface, they diverge or spread. Unlike concave mirrors, convex mirrors cause the light rays to diverge from the definite focal point. 

Types of images – from virtual to diminishing: irrespective of the distance between the object and the convex mirror, the images formed are virtual, uprights, and diminished. The image appears erect and smaller too compared to the actual size of the object. The image also appears on the rear side of the mirror. When you trace it backward, the virtual image forms through the intersection of diverging rays. 

View–Wide: Convex mirrors have an incredible feature to offer a broad canvas of view. This is because they possess an outwardly curved shape, and thus convex mirrors capture a wider area in reflection in comparison with flat and concave mirrors. Due to this, concave mirrors are used whenever there is a need for a larger perspective and a more expansive view. These can be large grounds for parking, sporting, meeting, and intersections, and where security, surveillance, and monitoring are involved 

Image – magnitude, and distance: convex mirrors are known to produce virtual images that are closer to the mirror than the object. The image that is formed by convex mirrors looks diminished and gives an impression of being smaller than the object’s real size. Due to this reduction, in the size of the image, a more expansive area can be captured for reflection.In summary, through convex mirrors, the light diverges as it strikes the reflecting surface The Convex mirrors always result in diminished, erect, and virtual images, regardless of the distance between the mirror and the object. 

Ray Diagram of Convex Mirror 

The Ray diagram of convex mirror is shown below along with the object placing. 

Object at Infinity: A point-sized image is generally formed at the principal focus behind the convex mirror.   

Object is kept between Infinity and Pole: If the object is placed in between the pole and infinity of a convex mirror, a diminished, erect, and virtual image at the pole is located in mid-point, focus, and pole.  

It is the complete description of the ray diagram of convex mirror when the object was placed at various points. 

Image Formation by convex mirrors and concave mirrors 

As we dwell deeper into the ray incidence on concave and convex mirrors, it becomes easier for us to ascertain and understand the characteristics and behavior of light rays. This is particularly helpful in building precise ray diagrams and analyzing image formation processes. 

Oblique Incidence: When a ray hits the mirror at its pole, its reflection is oblique, forming the same angle as the principal axis. This ensures the angle of incidence is equal to the angle of reflection, thus extending the symmetry of the reflected rays. 

Parallel Incidence: When a ray that is parallel to the principal axis hits the concave mirror or a convex mirror, it takes a definite trajectory. If it is a concave mirror, the ray goes through the focus on the principal axis. If it is for a convex mirror, the reflected ray is born out of the focus on the same side as the incident ray. 

Focus Incidence: When a ray passes through the focus and hits the surface of a concave mirror or a convex mirror, it will be seen traveling parallel to the principal axis. This is the same for both concave and convex mirrors. 

Centre of Curvature Incidence: When a ray travels through the center of curvature of a spherical mirror it will retrace its path after reflection. This is nothing but going through reflection and following the exact similar path in the opposite direction, when the ray touches the centre of the curvature. 

Convex and concave mirrors – important aspects 

Pole: The center point of any spherical mirror from where all measurements are made 

Aperture: An aperture of a mirror is an origin point of reflection of light 

Principal axis: This is an imaginary line passing through the optical center and from the center of curvature of a mirror. Generally, measurements are taken based on this line 

Centre of Curvature: this is a point in the center of the surface of a mirror and goes through the mirror curve, having the same tangent and curvature at the point. 

The radius of Curvature: This is the linear distance between the pole and the center of curvature. 

Principal Focus: This is the Focal Point and is there on the mirror axis. 

Focus: It is a point on the principal axis where light rays parallel to the principal axis come together after reflecting from the mirror. 

Examples of Concave Mirrors 

The examples of concave mirrors are listed below, 

Shaving and other domestic mirrors 

Telescopes 

Ophthalmology 

Vehicles as headlights 

solar furnaces 

Examples of Convex Mirrors 

The examples of convex mirrors are listed below, 

Office space, industrial complexes, stores, healthcare, and residential buildings 

In vehicles as rear-view mirrors 

Security purposes 

As magnifying glasses 

Large public spaces and grounds 

In the above article, we have provided a comprehensive description of both Concave and Convex Mirrors. We hope this article cleared the complete information of Ray Diagrams of concave mirrors and ray diagrams for convex mirrors and the differences. Besides, the types of mirrors, use of convex mirrors, use of concave mirrors. 

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[kaizenengineering]

https://jpst.it/3MlFa

To minimize weight, the Saddles Manufacturing Company in India on suspension bridge towers may have huge steel castings assembled in one piece (Fig. 15.36). The permitted lateral pressures on the cables, which depend on the saddle's radius of curvature, can help define the saddle's size. Additional saddles of a unique design might be necessary at side piers to deflect the anchor-span cables to the anchorages. At the anchorages, splay saddles can also be required.

[mysticstronomy]

HOW LOW-MASS BLACK HOLE BEND SPACE THE MOST??

Blog#250

Saturday, December 3rd, 2022

Welcome back,

one of the most mind-bending concepts about the universe itself is that gravity isn’t due to some unseen, invisible force, but comes about because the matter and energy in the universe bends and distorts the very fabric of space itself. matter and energy tell space how to curve, and that curved space lays out the path upon which matter and energy move. the distance between two points isn’t a straight line, but a curve determined by the fabric of space itself.

so where would you go if you wanted to find the regions of space that had the greatest amount of curvature? you’d pick the locations where you had the most mass concentrated into the smallest volumes: black holes. but not all black holes are created equal. paradoxically, it’s the smallest, lowest-mass black holes that create the most severely curved space of all. here’s the surprising science behind why.

When we look out at the Universe, particularly on large cosmic scales, it behaves as though space were virtually indistinguishable from flat. Masses curve space, and that curved space deflects light, but the amount of deflection is minuscule even for the most concentrated amounts of mass we know of.

The solar eclipse of 1919, where the light from distant stars was deflected by the Sun, caused the path of light to bend by less than a thousandth-of-a-degree. This was the first observational confirmation of General Relativity, caused by the largest mass in our Solar System.

Gravitational lensing goes a step beyond that, where a very large mass (like a quasar or galaxy cluster) bends space so severely that the background light gets distorted, magnified, and stretched into multiple images. Yet even trillions of solar masses cause effects on scales of tiny fractions-of-a-degree.

But it’s neither our proximity to a mass nor the total amount of mass that determines how severely space is curved. Rather, it’s the total amount of mass that’s present within a given volume of space. The best way to visualize this is to think about our Sun: a 1 solar-mass object with a radius of about 700,000 kilometers. At the very limb of the Sun, 700,000 km from its center, light deflects by about 0.0005 degrees.

Originally published on bigthink.com

COMING UP!!

(Wednesday, December 7th, 2022)

"WHAT CAN DEFEAT A BLACK HOLE??"

[yourmakemachineblog]

The method of shaft calibration for automatic measurement of C-type hydraulic press 1) The mathematical model of axis bending of shaft parts is established. The curve equation of axis bending is established, and the curvature, deflection and deflection of curve are calculated in the curve equation.  (2) In order to detect and fit the axis bending deformation, several equidistant sections are taken along the axis direction, and the axis is rotated to detect the data along the radius direction of the points on the outer surface of the shaft section.  (3) The straightening correction amount of shaft parts transforms the pressure straightening process into a simple deflection load curve model.  Zaozhuang Make Machinery Co., Ltd. is a company specializing in the production of hydraulic press equipment, C-type hydraulic press, four column hydraulic press, gantry hydraulic press, hydraulic bending machine and other styles, HP-63C, HP-100, HP-150, HP-200 and other models can be selected. We can customize the press according to the requirements of customers, welcome new and old customers to buy! (The picture below shows the customized C-type hydraulic press made by Zaozhuang Make Machinery Co., Ltd. for Egyptian customers) https://www.instagram.com/p/CIC55MDHkFk/?igshid=8zq2zooijx8b

[poolcueguide]

Best Pool Cues Frequently Asked Questions

POOL CUES FAQs

Pool Cue Guide 2887 Jadewood Drive Chicago, IL 60601 Phone: 224-366-6227 Website: https://poolcueguide.com/pool-cues-faqs/ Google Site: https://sites.google.com/site/bestpoolcuesintheworld/pool-cues-questions Google Folder: https://drive.google.com/drive/folders/1wDbcsoo974uaXfWadGqsRWX5Kp1reauB

How to replace pool cue tip ?

https://poolcueguide.com/pool-cues-faqs/#How_to_replace_pool_cue_tip You can replace the existing pool cue tip with a new one in four simple steps. In the first step, you remove the old tip. In the second step, you prepare the ferrule surface for the new one. In the third step, you install the new tip after sanding its bottom surface. In the fourth step, you customize its shape and hardness factors using the tip tool. Step 1 – Old Pool Cue Tip Removal The tip may have the support of a tip holder made of plastic aluminum. You need to remove that before taking out the tip. You can use the pliers to take it out. Make sure you don’t cause any damages to the sides of the ferrule top while removing it. Leather Tip: You can use a sharp blade or pliers to cut/pull out the existing leather tip from the metal cap at the end of the ferrule. Phenolic Tip: You can use the pliers to remove the Phenolic pool cue tip easily from the top of the ferrule. Step 2 – Prepare the Ferrule Surface Remnant Removal: The old leather tip may have left some remnants at the top. You can use the leather burnishing pad to take out the remnants completely. It will also eliminate the glue, dirt and other contaminant deposits at the top. Surface Sanding: Use the 80 grit sandpaper to sand the ferrule top that holds the tip. The surface should become even after you have completed the sanding. Surface Cleaning: Apply three to four drops of vinegar or nail polish remover on the top and rub with a clean tissue paper. Allow the liquid to dry out. Now, the top is ready for the new cue tip. Step 3 – New Pool Cue Tip Installation Bottom Sanding: Take the new pool cue tip and place it on the 80 grip sandpaper with the bottom down. Rub it gently until the surface evens out. Gluing: The glue you choose should have fast drying and impact resistance property. It should allow the two pieces (the tip and the ferrule top) to align accurately (assuming it takes about four to six seconds to align). The average drying time for good quality glue is 15-18 seconds. Apply the glue to the pool cue tip bottom and the ferrule top and align the two. Make sure the glue doesn’t spill over to the sides. Cue Cleaning: Once the glue becomes dry and the bonding between the ferrule top and cue tip is tight, you can use a soft tissue paper to clean the tip and the ferrule. You can use the nail polish remover to clean up any residual glue and dirt. Step 4- New Cue Tip Shaping Sanding: You can use the 80 grit sandpaper to rub the top and the side of the new tip until it attains the shape and hardness you need. Shaping: Alternately, you can use the tip shaper tool. The U-shaped tool can perform multiple functions of sanding, shaping (dime and nickel) and trimming. The dime gives optimum shape to the tip with medium hardness value. The contact surface between the tip and the cue ball will be optimum for accuracy and speed. On the other hand, the nickel radius cue tip is useful for generating more side-spin. The curvature of the ball movement will remain the same for both the types. Hardening: The shaper tool can also help harden the tip according to your specific requirements. The recommended hardness level is medium.

How Pool Cues are made ?

https://poolcueguide.com/pool-cues-faqs/#How_Pool_Cues_are_made Pool cues are made of pure wood, graphite, fiberglass, or the combination of the three materials. The initial manufacturing process may happen on the CNC machines for the pattern/inlay cutting, axial substitution, inlay designing, pool cue construction and surface finishing. The 4th-axis method is stated to be the most advanced technology in the making of professional pool cues. Currently, the pool cues are made into one-piece, two-piece, and three-piece designs. One-Piece Pool Cues One-piece pool cues have no joints, but they may use push-on-extension to keep the size compact for portability. · Material: The wood used for one-piece pool cue could be machine spliced hardwood, Maplewood, ash-wood, ebony, rosewood and other exotic species. High-end pool cues are handmade with ash-wood as the standard raw material. · Anatomy: The diameter of the cue increases from the tip to the butt evenly. The only parts to assemble with the main shaft are the tip, ferrule and the butt. There are no wraps on the pool cue. The fiber ferrule has the properties of shock-proof construction and high energy-transfer ratio from the butt, passing through the shaft onto the tip. The tip is made of high-quality leather for enhanced accuracy, zero deflection, and optimum speed. The butts could be made from ivory, brass or other metal alloys Two-Piece Pool Cues Materials: The materials that go into the making of the two-piece pool cues are Maplewood, fiberglass or graphite. The joints are made of metals like steel, brass or copper. The ferrule is made of fiber and the cues use nylon wrap with and leather tip. Graphite pool cues are made of polycarbonate ferrule, Veltex–grip wrap and leather tip. The composite pool cues are made from the combination of wood, fiberglass, and graphite with metallic joints and fiber/polycarbonate ferrule. Anatomy: The materials used in the two-piece pool cue are the maple wood and fiberglass. The Phenolic resin is another common material. The leather tip has a diameter of 12mm.The shaft has cone taper which decreases from the joint to the ferrule. The pool cue is split into two detachable parts for easy portability. Mass production of cues depends on the CNC machines and the hand-assembly. Three-Piece Pool Cues Materials: Some of the materials that go into the making of three-piece pool cue are maple wood, ash wood, hard wood etc, fiberglass, carbon fiber, aluminum, brass and other metal alloys. The cue has pro taper. The joint between the butt and the shaft has ABS material. Most of the 3-piece pool cues have wraps for grip. The design of the cue incorporates weight adjustable system for professional players. The cues have two joints compared to a single joint in the two-piece cues. Multiple coats of varnish on the cue help protect it from warping. Anatomy: The anatomy of a 3-piece has a forearm and a wrap that make up the shaft. The ferrule/collar has ivory, stainless steel, wood, or polycarbonate material. The butt and the inlay sections play a key part in balancing the pool cue weight increasing the stability of the cue. The pool cue joint rings are made of metal alloys, fiber, ivory or wood. They provide stability and enhance the aesthetic appeals of the cue. Mass production of the cues depends on the CNC machines and the hand-assembly procedures.

Are pool cues allowed on airplanes?

https://poolcueguide.com/pool-cues-faqs/#Are_pool_cues_allowed_on_airplanes The airline authorities don’t allow the pool cues as part of the carry-on baggage, but they do permit them in the form of checked bags. Most of them have listed the inventory items in their security and safety guidelines in conformance to the Transportation Security Administration standards and regulations.

How do you choose a Pool Cue?

https://poolcueguide.com/pool-cues-faqs/#How_do_you_choose_a_Pool_Cue The basic parameters of pool cue selection are related to the properties of the tip, ferrule, shaft, wrap, joints and the inlays. The material, design, construction, dimension and the weight of the cues are the most important contributors to the structure and functionality. Beginner Pool Cues The materials pool cues for the beginners are maple wood, Irish linen, leather, rubber and synthetic fiber. Cue Shaft: Maple wood with the pro-taper design is recommended to provide even weight balance. It should have minimum squirt (deflection) effect. It is the angle of deviation taken by the cue–ball after the cue strikes it. It may not be possible to avoid squirt, but the shaft design can reduce its value to the minimum. The playability factor naturally increases with a decrease in squirt. Radial lamination on the shaft can help increase the efficiency and flexibility. The tensile strength of the shaft is evenly distributed along the length and diameter. The shaft gives enhanced control over the cue when you strike the cue–ball. You may also choose the shafts with the standard taper that has gradually decreasing diameter from the bumper to the ferrule edge. Starting with the wooden shaft is preferred over fiberglass or carbon fiber since it can withstand shocks from accidental fall. Cue Ferrule: The material used for the beginner pool cue ferrule can be high-density hardwood, carbon fiber, polycarbonate or Maplewood. It is better to avoid brass and other metal alloys since they are meant for the advanced users. The ferrule is the connecting medium between the shaft and the tip. The capped design protects it from cracks. The threaded connector is better than gluing for durability and strength. The tenon size should be preferably large for enhanced connectivity with the tip and the cue–ball. Cue Tip: The cue tip plays a key role in shock absorption, ball spin control, impact, consistency, precision, shot variation and the ball jump. Medium hardness is preferred for the beginners as it helps in mastering the ball control and playing shots with minimum deflections. You may opt for carbon fiber, leather or Phenolic materials. Cue Wrap: The Irish linen on the cue wrap can provide the best grip while playing in the initial stages. It is also good in absorbing sweat. You can grip the cue at different positions without losing control at any point. Sliding the cue between your fingers becomes simple and smooth. Cue Bumper: The rubber bumper allows you to have better hold and control over the cue in the beginning. Bumper with screws is easy to replace than the ones which use glue. Opting for a used pool cue will make your selection economical and technically feasible. Your trainer will be able to help you choose the best-used cues based on their design and construction of the parts described above. Intermediate Pool Cues The design of the intermediate level best pool cues has better functionality compared to the beginner models. For example, the shaft and tip designs allow you to play better follow shots, draw shots and the stop shots. They also allow you to have better control over the hits passing through the central axis of the cue ball. You can vary the stroke speed depending on the distance between the cue-ball and the first object ball. · Cue Shaft: The cue shaft of the intermediate level cue can be Canadian maple, ash wood or the composite material having fiberglass at the exterior and Canadian maple at the core. They provide better accuracy of shot angles and improved control over the cue. The standard taper is better than pro-taper. Avoid the double–taper as it is meant for the expert level shafts. Enhanced cue-ball spin allows you to play from varied angles and get the desired results accurately. You can control the final position of the play ball which prepares the ground for the next shot. · Cue Ferrule: The material for the intermediate cue ferrule can be carbon fiber, wood or fiberglass. Titan and PVC are the suggested materials for lightweight and better flexibility. The threaded connectors provide accurate co-axial alignment with the shaft. The taper of the ferrule should be preferably standard or pro. Opt for a relatively higher tenon to have better connectivity with the cue-ball. Slip-on type of ferrule connects to the shaft and the tip without threads. The ferrule should be resistant to shocks and chalk. Polishing should be smooth, and maintenance should be simple. It should be able to transfer the maximum of energy from the shaft to the tip for all types of pool cue shots you play. · Cue Tip: At the intermediate level, it is better for you to choose the leather tip with medium to the higher level of hardness. They will allow better control over the left and right ENGLISH for accuracy in controlling the angle of squirt and spin. Reverse spin and topspin control get better with the optimized hardness levels. Consistency in your shot speed and types makes the medium hardness ideal for intermediate level pool cues. The hardness factor of the tip can be between 66.3 and 79.8. The type of lamination is another factor that determines the hardness. You may choose the tip shape to be dime or nickel. Dime shape is used to generate extra spin, while the nickel shape gives you better control with more contact space with the cue–ball. · Cue Wrap: The pool cue wrap provides grip over the shaft and power on the shot. Rubber wraps are recommended if your hands sweat more. Leather wraps offer good hold. But they can become sticky with sweat. If you wish to have a good grip on the smooth movement of the shaft between your fingers, it is better to opt for rubber or Irish-linen. · Cue-Bumper: The synthetic rubber cue bump with the screw is always the recommended material for beginner and intermediate level pool cues. At the intermediate level, you can afford to get the new cues made from maple wood, fiberglass, carbon fiber or the composite materials. Two-piece cues are better at this stage as they help in improving your adaptability to the professional level. Advanced Pool Cues Advanced pool cues are made for the players who wish to avoid deflection of the cue ball. They increase the accuracy, spin control, taper strength, consistency, vibration and speed control. Cue Shaft: The recommended materials for the advanced cue shaft are maple, carbon fiber and fiberglass. Having a foam core at the top of the shaft can reduce the weight and reducing the deflection levels. It can also increase the performance. Having a carbon fiber at the core helps in enhancing the performance and feedback. It allows you to vary the orientation of your shots and maintain the efficiency of the follow shots and the draw shots. The straight path of the cue ball can be controlled by varying your shot selection, regardless of the distance between the cue-ball and the first object ball. The composite shaft (wooden top with carbon fiber core) can also improve the radial consistency and playing style for higher efficiency. Double taper can improve the accuracy while playing complex shots. The shafts have the threaded connectors at both the ends (with the top section of the cue and the ferrule). However, this type of taper needs highest level of experience on part of the player, since the design may make it more complex for handling the shaft. On the other hand, a standard taper or the conical taper helps in getting better control over the smooth flow of the shaft between your fingers. Pivot Point: The pivot point on the shaft can help in getting better control over the shots. The manufacturers of the advanced cue shafts between 11” and 14” for increasing the acceleration and accuracy. You need to check the ratio between the bridge length of the shaft and the pivotal point to get the maximum efficiency pool ball cue. Cue Ferrule: At the advanced level, you may opt for brass or other metal alloy. It has a screw-based core which attaches to the shaft. It enhances the performance and reduces the deflection angle further. But its weight is relatively more compared to the other materials like carbon fiber, fiberglass and even wood. Ivory gives better hits and feedback to the shaft. You can also opt for JUMA which is becoming an alternative for ivory with most of the properties being the same. You need to opt for capped and threaded tenon, optimum weight and enhanced performance. Cue Tip: The tips for the advanced pool cues are preferably made of higher hardness factors. They can give you better control over your shots. They also improve the playability features. Nickel shaped radius is supposed to provide better spin control and optimum contact point with the cue–ball. The number of layers on the cowhide leather determines the hardness ratio. Laminated tips with improved performance can increase the efficiency of the pool cue. The cue tip has to be scuffed with an abrasive material having coarse grits. It helps in getting better chalk holding and control over the cue–ball. The other recommended materials for the tip are the carbon fiber and Phenolic. The selection of the tip also depends on the playing and breaking techniques you wish to use in the game. The hardness factor above 83.2 is the most recommended value for the advanced cue tips. Make sure the tips have no chemical compositions, since they can decrease the lifespan considerably. Cue Wrap: The recommended material for the pool cue wrap is the natural leather. It has the characteristic of providing the optimum grip over the shaft, while making it easier to slide it between your fingers. Cue Bumper: The recommended material for the cue bumper is synthetic rubber for enhanced grip and ease of control. Cue Rings: Having the metallic, fiber and JUMA rings at the joints can increase the aesthetic appeals of the pool cue. It can also enhance the joint efficiency and axial alignment of all the connecting points in the pool cue.

What Pool Cues do Pros Use?

https://poolcueguide.com/pool-cues-faqs/#What_Pool_Cues_do_Pros_Use The advanced parameters that make a professional pool cue are the shaft design, ferrule construction, tip characteristics and the overall quality. You may choose any model and brand that conforms to the following characteristics. Shaft Characteristics Front End Mass: Pros use cue shafts that have the lightest front end mass. It gives better control over the energy transfer from the shaft onto the ferrule. The accuracy also increases considerably. Grain Density: Radial lamination of the shaft increases the grain density to the most optimum level. Straight grains are recommended as they help streamline the flow of energy. The conversion ratio of the energy at the tip also increases. Ash shafts, maple shafts, and Purple Heart shafts can have the most efficient grain density and direction. Material Strength: The material strength of the shaft depends on the core material and the radial consistency. Shafts with carbon fiber reinforced core can help in shock absorption. They also provide better top and side-spin to the cue–ball. Shaft Weight: The taper type determines the shaft weight from the bumper to the ferrule end. Standard taper results in evenly distributed weight reduction. It gives better control over the cue. Shaft Shape: The most commonly used shaft shapes are V, W, P, S and R. The V–shaft is slim and light in weight. S-shaft is flexible with high grain density. The W-shaft is recommended for higher stiffness and penetration for the cue–ball. The P-shaft is the most recommended one for the professional cues. Ferrule Characteristics Bronze or JUMA-capped ferrules are the most recommend modes for the professional pool cues. The Phenolic ferrule is ideal for jump cues. T-Capped ferrule provides maximum hit speed and energy transfer from the shaft onto the tip. Tip Characteristics Burnished Side: The pre-burnished side of the cue tip provides better control over the side and top-spin of the cue-ball. It also optimizes the contact space between the tip and the cue-ball. Tip Size: Oversized tip can result in better energy transfer, spin direction control and better grip over the cue-ball. Tip Diameter: The diameter of 13-mm with nickel style of the radius is the most recommended pool cue tip for the professionals. Tip Hardness: Hardness factor 2 and above is the most recommended value for the professional pool cue. Joint Characteristics The screw types of joints are the best ones for the shaft and ferrule, shaft and the butt, butt and the bumper as well as the inlays. They help in easy replacements and better maintenance.

What weight pool cue is best?

https://poolcueguide.com/pool-cues-faqs/#What_weight_pool_cue_is_best The average pool cue weight from the standard and professional brands is stated to be between 18 and 21 ounces. The 20-ounce is recommended for beginners. The 19.5-ounce is recommended for intermediate level players. Professionals may opt for lighter cues for speed and heavier ones for a better break.

What are the Best Brands of Pool Cues?

https://poolcueguide.com/pool-cues-faqs/#What_are_the_Best_Brands_of_Pool_Cues Anyone looking to buy a new pool cue will be flabbergasted to find hundreds of brands they can choose from. Since your pool cue is the one item that can determine how well you play billiards, it is important to find a trusted and reliable brand to buy your pool cue from. The following brands are some of the best ones out there as they are known for their high-quality products and their ingenuity when it comes to pool cues. McDermott This Wisconsin based brand has had several decades of experience making pool cues as they first started in 1975. McDermott makes use of top quality wood to create perfectly crafted pool cues. Their pool cues also go through around 150 processes to ensure every product meets the company’s high standards. Their G series cues are the best ones to be released yet. Schon Another Wisconsin based company, Schon, was founded in 1981. Since the company’s inception, the brand has dedicated itself to perfectly crafting each cue and avoiding mass production completely. This ensures that each cue is made with complete accuracy and precision for the best playing experience. Meucci Considered to be one of the first pool cue makers in the US, Meucci has always made use of extremely high-quality woods and prides itself on its unique ingenuity (with its recent release of the carbon fiber shaft). Meucci cues are widely known for providing the user with the best amount of control. Meucci has become a household name since it first began crafting pool cues. Joss Joss is a family company that originated in 1968. Many famous movies have featured Joss cues as to their props, but the cues are not just beautiful pieces of work, they are also incredibly precise and provide players with accurate hits when playing. Why use pool cue chalk? https://poolcueguide.com/pool-cues-faqs/#Why_use_pool_cue_chalk The increase in the friction coefficient between the tip and the cue-ball can avoid miscued shots due to slipping and help in enhancing the grip over the ball.

[siva3155]

300+ TOP RAILWAY ENGINEERING Objective Type Questions and Answers

RAILWAY ENGINEERING Multiple Choice Questions :-

1. The rail is designated by its a) length b) weight c) cross-section d) weight per unit length Ans: d 2. Two important constituents in the com-position of steel used for rail are a) carbon and silicon b) manganese and phosphorous c) carbon and manganese d) carbon and sulfur Ans: c 3. The standard length of rail for Broad Gauge and Meter Gauge are respectively a) 12 m and 12 m b) 12 m and 13 m c) 13 m and 12 m d) 13 m and 13 m Ans: c 4. The following tests are conducted for rails: i) falling weight test ii) tensile test iii) hammer test The compulsory tests are a) only (i) b) (i)and(ii) c) (ii) and (iii) d) (i) and (iii) Ans: b 5. Largest dimension of a rail is its a) height b) foot width c) head width d) any of the above Ans: a 6. Largest percentage of material in the rail is in its a) head b) web c) foot d) head and foot both Ans: a 7. The purpose of providing fillet in a rail section is to a) increase the lateral strength b) increase the vertical stiffness c) avoid the stress concentration d) reduce the wear Ans: c 8. The cross-sectional area of 52 kg flat footed rail is a) 6155 mm2 b) 6615 mm2 c) 7235 mm2 d) 7825 mm2 Ans: b 9. 52 kg rails are mostly used in a) Broad Gauge b) Meter Gauge c) Narrow Gauge d) both (a) and (b) Ans: a 10. Tensile strength of steel used in rails should not be less than a) 450 MPa b) 500 MPa c) 700 MPa d) 850 MPa Ans: c 11. Head width of 52 kg rail section is a) 61.9 mm b) 66.7mm c) 67mm d) 72.33 mm Ans: c 12. 60 R rails are mostly used in a) Broad Gauge b) Metre Gauge c) Narrow Gauge d) none of the above Ans: b 13. Ordinary rails are made of a) mild steel b) cast iron c) wrought iron d) high carbon steel Ans: d 14. The main function of a fish plate is a) to join the two rails together b) to join rails with the sleeper c) to allow rail to expand and contract freely d) none of the above Ans: a 15. Number offish bolts per fish plate is a) 2 b) 4 c) 5 d) 6 Ans: b 16. Fish plate is in contact with rail at a) web of rail b) fishing plane c) head of rail d) foot of rail Ans: b 17. Gauge is the distance between a) center to center of rails b) running faces of rails c) outer faces of rails d) none of the above Ans: b 18. Which of the following factors govern the choice of the gauge ? i) volume and nature of traffic ii) speed of train iii) physical features of the country The correct answer is a) only (i) b) both (i) and (ii) c) both (ii) and (iii) d) (i), (ii) and (iii) Ans: d 19. For developing thinly populated areas, the correct choice of gauge is a) Broad Gauge b) Meter Gauge c) Narrow Gauge d) any of the above Ans: c 20. Due to battering action of wheels over the end of the rails, the rails get bent down and are deflected at ends. These rails are called a) roaring rails b) hogged rails c) corrugated rails d) buckled rails Ans: b 21. The slipping of driving wheels of locomotives on the rail surface causes a) wheel burns b) hogging of rails c) scabbing of rails d) corrugation of rails Ans: a 22. The width of foot for 90 R rail section is a) 100 mm b) 122.2 mm c) 136.5 mm d) 146.0 mm Ans: c 23. The height of the rail for 52 kg rail section is a) 143 mm , b) 156 mm c) 172 mm ' d) 129mm Ans: b 24. The formation width for a railway track depends on the i) type of gauge ii) number of tracks to be laid side by side iii) slope of sides of embankment or cutting The correct answer is a) only (i) b) both (i) and (ii) c) both (i) and (iii) d) (i), (ii) and (iii) Ans: b 25. The formation width for a single line meter gauge track in embankment as adopted on Indian Railways is a) 4.27 m b) 4.88 m c) 5.49 m d) 6.10 m Ans: b 26. The side slope of embankments for a railway track is generally taken as a) 1:1 b) 1.5:1 c) 2:1 d) 1:2 Ans: c 27. The formation width for a double line Broad Gauge track in cutting (excluding drains) as adopted on Indian Railways is a) 6.10 m b) 8.84 m c) 10.21m d) 10.82 m Ans: c 28. The total gap on both sides between the inside edges of wheel flanges and gauge faces of the rail is kept as a) 10mm b) 13mm c) 16mm d) 19 mm Ans: d 29. Creep is the a) longitudinal movement of rail b) lateral movement of rail c) vertical movement of rail d) difference in level of two rails Ans: a 30. Anti creep bearing plates are provided on a) bridges and approaches b) joints c) both (a) and (b) d) none of the above Ans: d 31. Study the following statements regarding creep. i) Creep is greater on curves than on tangent railway track, ii) Creep in new rails is more than that in old rails, iii) Creep is more on steep gradients than on level track. The correct answer is a) only (i) b) (i)and(ii) c) (ii) and (iii) d) (i), (ii) and (iii) Ans: b 32. The maximum degree of curvature for Meter Gauge is limited to a) 10° b) 16° c) 30° d) 40° Ans: b 33. Staggered joints are generally provided a) on curves b) on straight track c) when two different rail sections are required to be joined d) none of the above Ans: a 34. When the rail ends rest on a joint sleeper, the joint is termed as a) supported rail joint b) suspended rail joint c) bridge joint d) base joint Ans: a 35. Which of the following types of sleepers is preferred on joints ? a) CST-9 sleeper b) steel trough sleeper c) wooden sleeper d) concrete sleeper Ans: c 36. Minimum depth of ballast cushion for a Broad Gauge wooden sleeper of size 275x25x13 cm with 75cm sleeper spacing is a) 15 cm b) 20 cm c) 25 cm d) 30cm Ans: c 37. Sleeper density in India is normally kept as a) M + 2 to M + 7 b) MtoM+2 c) M + 5toM+10 d) M where M is the rail length in meters. Ans: a 38. For a Broad Gauge route with M+7 sleeper density, number of sleepers per rail length is a) 18 b) 19 c) 20 d) 21 Ans: c 39. Standard size of wooden sleeper for Broad Gauge track is a) 275x25x13cm b) 180x20x11.5 cm c) 225x23x13 cm d) 250x26x12 cm Ans: a 40. Composite sleeper index is the index of a) hardness and strength b) strength and toughness c) toughness and wear resistance d) wear resistance and hardness Ans: a 41. Minimum composite sleeper index pres-cried on Indian Railways for a track sleeper is a) 552 b) 783 c) 1352 d) 1455 Ans: b 42. Dog spikes are used for fixing rail to the a) wooden sleepers b) CST-9 sleepers c) steel trough sleepers d) concrete sleepers Ans: a 43. Number of dog spikes normally used per rail seat on curved track is a) one on either side b) two outside and one inside c) one outside and two inside d) two outside and two inside Ans: b 44. The type of bearing plate used in all joints and on curves to give better bearing area to the rails is a) flat mild steel bearing plate b) mild steel canted bearing plate c) cast iron anti creep bearing plate d) none of the above Ans: b 45. Flat mild steel bearing plates are used a) for points and crossings in the lead portion b) with wooden sleepers at locations where creep is likely to be developed c) on all joints and curves d) on all the above Ans: a 46. The nominal size of ballast used for points and crossings is a) 25 mm b) 40 mm c) 50 mm d) 10mm Ans: a 47. At points and crossings, the total number of sleepers for 1 in 12 turnouts in Broad Gauge is a) 51 b) 62 c) 70 d) 78 Ans: c 48. Width of ballast section for Broad Gauge is a) 1.83 m b) 2.25 m c) 3.35 m d) 4.30 m Ans: c 49. The type of spike used for fixing chairs of bull headed rails to wooden sleepers is a) dog spike b) rail screw c) elastic spike d) round spike Ans: d 50. The sleepers resting directly on girder are fastened to the top flange of girder by a) hook bolts b) dog spikes c) fang bolts d) rail screws Ans: a 51. Number of keys used in CST-9 sleeper is a) 2 b) 3 c) 4 d) none of the above Ans: a 52. Loose jaws of steel trough sleepers are made of a) cast steel b) mild steel c) cast iron d) spring steel Ans: d 53. Number of cotters used in CST-9 sleepers is a) 2 b) 3 c) 4 d) 5 Ans: c 54. Pandrol clips cannot be used with a) wooden sleepers b) concrete sleepers c) CST-9 sleepers d) steel trough sleepers Ans: c 55. The desirable rate of change of cant deficiency in case of Metre Gauge is a) 20 mm/sec b) 35 mm/sec c) 55 mm/sec d) 65 mm/sec Ans: b 56. The limiting value of cant excess for Broad Gauge is a) 55 mm b) 65 mm c) 75 mm d) l00 mm Ans: c 57. The limiting value of cant gradient for all gauges is a) 1 in 360 b) 1 in 720 c) 1 in 1000 d) 1 in 1200 Ans: b 58. Normally the limiting value of cant is a) G/8 b) G/10 c) G/12 d) G/15 where G is the gauge. Ans: b 59. Vertical curves are provided where algebraic difference between grades is equal to or a) less than 2 mm/m b) more than 2 mm/m c) less than 4 mm/m d) more than 4mm/m Ans: d 60. The limiting value of cant deficiency for Meter Gauge routes is a) 40 mm b) 50 mm c) 75 mm d) 100 mm Ans: b 61. The steepest gradient permissible on a 2.5° curve for Broad Gauge line having ruling gradient of 1 in 200 is a) 1 in 250 b) 1 in 222 c) 1 in 235 d) 1 in 275 Ans: a 62. Normally maximum cant permissible in Meter Gauge is a) 75 mm b) 90 mm c) 140 mm d) 165 mm Ans: b 63. Cant deficiency occurs when a vehicle travels around a curve at a) equilibrium speed b) speeds higher than equilibrium speed c) speeds lower than equilibrium speed d) booked speed Ans: b 64. The compensation for curvature on gradient for Meter Gauge is given by a) 70/R b) 52.5/R c) 35/R d) 105/R where R is radius of curve. Ans: b 65. The shape of transition curve used by Indian Railways is a) cubic parabola b) spiral c) sine curve d) lemniscate of Bernoulli Ans: a Railway Engineering Interview Questions :- 67. A Broad Gauge branch line takes off as a contrary flexure from a main line If the superelevation required for branch line is 10 mm and cant deficiency is 75 mm, the superelevation to be actually provided on the branch line will be a) 10 mm b) 64 mm c) 85 mm d) 65 mm Ans: d 68. One degree of curve is equivalent to where R is the radius of curve in meters. a) 1600/R b) 1700/R c) 1750/R d) 1850/R Ans: c 70. Switch angle is the angle between a) the gauge face of the stock rail and tongue rail b) the outer face of the stock rail and tongue rail c) the gauge face of the stock rail and outer face of the tongue rail d) the outer face of the stock rail and the gauge face of the tongue rail Ans: a 71. Switch angle depends on i) heel divergence ii) length of tongue rail iii) flangeway clearance iv) throw of switch The correct answer is a) (i) and (ii) b) (ii) and (iii) c) (iii) and (iv) d) (i)and(iv) Ans: a 72. Maximum value of 'throw of switch' for Broad Gauge track is a) 89 mm b) 95 mm c) 100 mm d) 115 mm Ans: d 73. Stretcher bar is provided a) to permit lateral movement of the tongue rail b) to maintain the two tongue rails at the exact distance c) to ensure exact gauge at the toe of the switch as well as the nose of crossing d) to prevent any vertical movement between the wing rail and nose of crossing Ans: b 74. Which of the following methods of designation of crossing is mostly used in India ? a) center line method b) right angle method c) isosceles angle method d) none of the above Ans: b 75. If a is the angle of crossing, then the number of crossings 'N' according to right angle method is given by a) Vi cot(cc/2) b) cot(oc/2) c) cot(a) d) Vi cosec(a/2) Ans: c 76. Which of the following turnouts is most commonly used for goods train on Indian Railways ? a) 1 in 8'/2 b) 1 in 12 c) 1 in 16 d) 1 in 20 Ans: a 77. Lead of crossing is the distance from the a) heel of the switch to the toe of the switch b) heel of the switch to the theoretical nose of the crossing c) toe of the switch to the theoretical nose of crossing d) toe of the switch to the actual nose of crossing Ans: b 78. Number of switches provided on a Gaunt-letted track is a) 1 b) 2 c) 3 d) none of the above Ans: d 79. The correct relation between curve lead (CL), switch lead (SL) and lead of cros¬sing (L) is given by a) CL = L - SL b) L =CL-SL c) SL = L + CL d) L = (CL+SL)/2 Ans: b 80. In a scissors cross-over, the crossings provided are i) 2 obtuse angle crossings ii) 4 obtuse angle crossings iii) 4 acute angle crossings iv) 6 acute angle crossings The correct answer is a) (i) and (iii) b) (i)and(iv) c) (ii) and (iii) d) (ii) and (iv) Ans: b 81. The distance through which the tongue rail moves laterally at the toe of the switch for movement of trains is called a) flangeway clearance b) heel divergence c) throw of the switch d) none of the above Ans: c 82. Flangeway clearance is the distance a) between the adjoining faces of the running rail and the check rail near the crossing b) between the gauge faces of the stock rail and the tongue rail c) through which the tongue rail moves laterally at the toe of the switch d) none of the above Ans: a 83. Heel divergence is a) always less than flangeway clearance b) equal to flangeway clearance c) always greater than flangeway clearance d) sometimes greater than flangeway clearance Ans: c 84. Which of the following mechanical devices is used to ensure that route cannot be changed while the train is on the point even after putting back the signal ? a) detectors b) point lock c) iock bar d) stretcher bar Ans: c 85. The treadle bar is provided a) in the middle of the track a little in front of the toes of the tongue rail b) near and parallel to inner side of one of the rails c) at right angle to the rail d) near and parallel to inner side of both the rails Ans: b 86. The object of providing a point lock is a) to ensure that each switch is correctly set b) to ensure that the point may not be operated while the train is on it c) to detect any obstruction between and tongue rail d) none of the above Ans: a 87. Which of the following devices is used to transfer the wagons or locomotives to and from parallel tracks without any necessity of shunting ? a) triangle b) turntable c) traverser d) scotch block Ans: c 88. A triangle is used for a) changing the direction of engine b) transferring wagons to and from parallel tracks without shunting c) separating all the sidings and shunting lines from main lines d) preventing the vehicles from running off the track Ans: a 89. The height of the center of arm of a semaphore signal above the ground is a) 5.5m b) 6.5 m c) 7.5 m d) 8.5m Ans: c 90. The reception signal is i) outer signal ii) home signal iii) starter iv) advanced starter The correct answer is a) (i) and (ii) b) (ii) and (iii) c) (iii) and (iv) d) (i)and(iv) Ans: a 91. Yellow lighthand signal indicates a) stop b) proceed c) proceed cautiously d) none of the above Ans: c 92. When semaphore and warner are installed on the same post, then the stop indication is given when a) both arms are horizontal b) semaphore arm lowered but warner arm horizontal c) both semaphore and warner arms lowered d) none of the above Ans: a 93. In a shunting signal if the red band is inclined at 45° it indicates a) stop b) proceed c) proceed cautiously d) none of the above Ans: b 95. For the purpose of track maintenance, the number of turn out equivalent to one track km are a) 1 b) 2 c) 5 d) 10 Ans: d 96. A train is hauled by 4-8-2 locomotive. The number of driving wheels in this locomotive is a) 4 b) 8 c) 12 d) 14 Ans: b 97. To ensure exact gauge, the gauge tie plates are provided at a) toe of the switch b) nose of crossing c) both (a) and (b) d) none of the above Ans: c 99. On a single rail track, goods trains loaded with heavy iron material run starting from A to B and then empty wagons run from B to A. The amount of creep in the rails. a) will be more in the direction of B to A b) will be more in the direction of A to B c) will be maximum at the middle of A and B d) cannot be determined from the given data. Ans: b 100. For laying the railway track, materials required are A) Rails B) FishPlates C) Fish Bolts D) Bearing Plates The quantities required for one kilometer of Broad Gauge track will be Ans: b 102. Which of the following statements regarding ballast materials are correct? 1. Brick ballast has poor drainage characteristics. 2. Coal ash is not used as ballast with steel or cast iron sleepers. 3. Gravel ballast gives better performance on soft formation. 4. Sand ballast causes excessive wear on top of rail. Select the correct answer using the codes given below. Codes : Ans: d 104. Metal sleepers are superior to wooden sleepers with respect to a) cost b) life c) track circuiting d) fastening Ans: b 105. Which one of the following rail failures is caused by loose fish bolts at expansion joints? a) crushed head b) angular break c) split head d) transverse fissures Ans: a 106. For a 8° curve track diverging from a main curve of 5° in an opposite direction in the layout of a broad gauge yard, the cant to be provided for the branch track for maximum speed of 45 km/h on the main line and 'G' = 1.676 m is (Permitted cant deficiency for the main line = 7.6 cm) a) 0.168 cm b) -0.168 cm c) 7.432 cm d) 7.768 cm Ans: b 107. Consider the following statements: Automatic signalling system results in 1. greater risk 2. higher efficiency 3. avoidance of block instruments 4. higher operating cost Of these statements a) I and 2 are correct b) 3 and 4 are correct c) 1 and 4 are correct d) 2 and 3 are correct Ans: d 108. Wear of rails is maximum in weight of a) tangent track b) sharp curve c) tunnels d) coastal area Ans: b 114. A train is hauled by 2-8-2 locomotive with 22.5 tonnes and on each driving axle. Assuming the coefficient of rail-wheel friction to be 0.25, what would be the hauling capacity of the locomotive? a) 15.0 tonnes b) 22.5 tonnes c) 45.0 tonnes d) 90.0 tonnes Ans: b 115. A treadle bar is used for a) interlocking points and signal b) setting points and crossings c) setting marshalling yard signals d) track maintenance Ans: a 116. Consider the following statements about concrete sleepers. 1. They improve the track modulus. 2. They have good scrap value. 3. They render transportation easy. 4. They maintain the gauge quite satisfactorily. Of these statements a) 1 and 2 are correct b) 2 and 3 are correct c) 3 and 4 are correct d) 1 and 4 are correct Ans: d 117. What will be the curve lead for a 1 in 8.5 turnout taking off from a straight broad gauge track? a) 28.49 m b) 21.04 m c) 14.24 m d) 7.45 m Ans: a 118. Consider the following surveys. 1. Reconnaissance survey 2. Preliminary survey 3. Traffic survey 4. Location survey The correct sequence in which these surveys are conducted before the alignment of a track is finalised is a) 1,3,2,4 b) 1,3,4,2 c) 3,1,4,2 d) 3,1,2,4 Ans: d 119. The load on each axle of a locomotive is 22 tonnes. If the coefficient of friction is 0.2, then the hauling capacity due to 3 pairs of driving wheels will be a) 26.41 b) 19.81 c) 13.21 d) 6.61 Ans: c 120. In a B.G. railway track, the specified ruling gradent is 1 in 250. The horizontal curve of 3° on a gradient of 1 in 250 will have the permissible gradient of a) 1 in 257 b) 1 in 357 c) 1 in 457 d) 1 in 512 Ans: b 121. For a sleeper density of (n+5), the number of sleepers required for constructing a broad gauge railway track of length 650 m is a) 975 b) 918 c) 900 d) 880 Ans: c 122. If 'A' is the angle formed by two gauge faces, the crossing number will be a) tan A b) cot A c) sec A d) Arad Ans: b RAILWAY ENGINEERING Objective type Questions and Answers pdf free download :: Read the full article

[inhandnetworks-blog]

WiFi  Researchers Discover a New Mechanism for Guiding Light in Photonic Crystal Fiber

www.inhandnetworks.com

Coreless optical fiber: If a photonic crystal fiber is twisted, it does not require a core with a different refractive index to trap light at its center.

A team of scientists from the Max Planck Institute for the Science of Light in Erlangen has discovered a new mechanism for guiding light in photonic crystal fiber.

Photonic crystal fiber (PCF) is a hair-thin glass fiber with a regular array of hollow channels running along its length. When helically twisted, this spiraling array of hollow channels acts on light rays in an analogous manner to the bending of light rays when they travel through the gravitationally curved space around a star, as described by the general theory of relativity.

Optical fibers act as pipes for light. And just as the inside of a pipe is enclosed by a wall, optical fibers normally have a light-guiding core, whose glass has a higher refractive index than the glass of the enclosing outer cladding. The difference in the refractive index causes the light to be reflected at the cladding interface and trapped in the core like water in a pipe. A team headed by Philip Russell, Director at the Max Planck Institute for the Science of Light, is the first to succeed in guiding light in a PCF with no core.

Photonic crystals give butterflies their color and can also guide light

A typical photonic crystal consists of a piece of glass with holes arranged in regular periodic pattern throughout its volume. Since glass and the air have different refractive indices, the refractive index has a periodic structure. This is the reason these materials are called crystals—their atoms form an ordered, three-dimensional lattice as found in crystalline salt or silicon, for example. In a conventional crystal, the precise design of the 3D structure determines the behavior of electrons, resulting for example in electrical insulators, conductors and semiconductors.

In a similar manner, the optical properties of a photonic crystal depend on the periodic 3D microstructure, which is responsible for the shimmering colors of some butterfly wings, for example. Being able to control the optical properties of materials is useful in a wide variety of applications. The photonic crystal fibers developed by Philip Russell and his team at the Erlangen-based Max Planck Institute can be used to filter specific wavelengths out of the visible spectrum or to produce very white light, for example.

As is the case with all optical fibers used in telecommuni industrial cellular modem3g modem  cations, all conventional photonic crystal fibers have a core and cladding each with different refractive indices or optical properties. In PCF, the air-filled channels already give the glass a refractive index different from the one it would have if completely solid.

The holes define the space in a photonic crystal fiber

“We are the first to succeed in guiding light through a coreless fiber,” says Gordon Wong from the Max Planck Institute for the Science of Light in Erlangen. The researchers working in Philip Russell’s team have fabricated a photonic crystal fiber whose complete cross-section is closely packed with a large number of air-filled channels, each around one thousandth of a millimeter in diameter, which extend along its whole length.

While the core of a conventional PCF is solid glass, the cross-sectional view of the new optical fiber resembles a sieve. The holes have regular separations and are arranged so that every hole is surrounded by a regular hexagon of neighboring holes. “This structure defines the space in the fiber,” explains Ramin Beravat, lead author of the publication. The holes can be thought of as distance markers. The interior of the fiber then has a kind of artificial spatial structure which is formed by the regular lattice of holes.

“We have now fabricated the fiber in a twisted form,” c wireless networking  ontinues Beravat. The twisting causes the hollow channels to wind around the length of the fiber in helical lines. The researchers then transmitted laser light through the fiber. In the case of the regular, coreless cross-section, one would actually expect the light to distribute itself between the holes of the sieve as evenly as their pattern determines, i.e. at the edge just as much as in the center. Instead, the physicists discovered something surprising: the light was concentrated in the central region, where the core of a conventional optical fiber is located.

In a twisted PCF, the light follows the shortest path in the interior of the fiber

“The effect is analogous to the curvature of space in Einstein’s general theory of relativity,” explains Wong. This predicts that a heavy mass such as the Sun will distort the space surrounding it – or more precisely, distort spacetime, i.e. the combination of the three spatial dimensions with the fourth dimension, time – like a sheet of rubber into which a lead sphere is placed. Light follows this curvature. The shortest path between two points is then no longer a straight line, but a curve. During a solar eclipse, stars which should really be hidden behind the Sun thus become visible. Physicists call these shortest connecting paths “geodesics”.

“By twisting the fi wired  ber, the ‘space’ in our photonic crystal fiber becomes twisted as well,” says Wong. This leads to helical geodesic lines along which light travels. This can be intuitively understood by taking into account the fact that light always takes the shortest route through a medium. The glass strands between the air-filled channels describe spirals, which define possible paths for the light rays. The path through the wide spirals at the edge of the fiber is longer than that through the more closely wound spirals in its center, however, resulting in curved ray paths that at a certain radius are reflected by a photonic crystal effect back towards the fiber axis.

A twisted PCF as a large-scale environmental sensor

The more the fiber is twisted, the narrower is the space within which the light concentrated. In analogy to Einstein’s theory, this corresponds to a stronger gravitational force and thus a greater deflection of the light. The Erlangen-based researchers write that they have created a “topological channel” for the light (topology is concerned with the properties of space which are conserved under continuous distortion).

The researchers emphasize that their work is basic research. They are one of the very few research groups working in this field anywhere in the world. Nevertheless, they can think of several applications for their discovery. A twisted fiber which is less twisted at certain intervals, for example, will allow a portion of the light to escape to the outside. Light could then interact with the environment at these defined locations. “This could be used for sensors which measure the absorption of a medium, for instance.” A network of these fibers could collect data over large areas as an environmental sensor.

Publication: Ramin Beravat, et al., “Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light,” Science Advances 25 Nov 2016: Vol. 2, no. 11, e1601421; DOI: 10.1126/sciadv.1601421

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[physicsclasses]

1)Name the Physical quantities to be kept constant for Ohm’s law to be true. 2)State the Principle of a potentiometer. (The students say that potential drop is proportional to length but the constant quantities are not mentioned) 3)How can we increase the sensitivity of a potentiometer? 4)Define figure of merit of a galvanometer. Which has more resistance – a galvanometer or a milliammeter? 5)How does an LED emit light? 6)What is the difference between an ordinary diode and an LED? 7)Define principal axis of a convex lens? What happens to the focal length of a concave mirror if it is immersed in water? 8)What are the factors affecting the intrernal resistance of a cell? What are the difference between primary and secondary cell? 9)Why can’t we use a dry cell for starting a car? Hints/Answers length, area of cross section,temperature Ans) The potential drop across any length of a conductor of uniform cross section and composition carrying a constant current is directly proportional to the length. increasing the length of potentiometer wire, decreasing the current, decreasing the potential gradient Current for unit deflection galvanometer The energy released during recombination of electrons and holes across the junction is responsible for the release of light by LED In ordinary diode the energy emitted during recombination of electrons and holes is in the invisible region of the em spectrum but in the case of LED, the energy is in the visible region. Straight line joining the centres of curvature of the lens.. The focal length of mirror does not change by changing the medium. Their is a pure geometrical relationship between the radius of curvature and focal length and the relation does not include any term depending on refractive index. the nature of electrolyte, the concentration of electrolyte, temperature, distance between electrodes, area of electrodes Primary cell cannot be recharged, secondary cells can be recharged; secondary cells have less internal resistance than primary cells. Due to the high internal resistance of a dry cell, it won’t be able to provide the current sufficient to start the car.

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[tutoroot]

What is the Image Formation by Convex Mirrors and Concave Mirrors? 

In Physics, students often encounter the term, spherical mirrors, while learning about how light is deflected and at what angles. Several concepts and chapters are directly derived from it. There are two types of spherical mirrors, Convex Mirrors and Concave Mirrors. 

Convex mirrors and concave mirrors differ in their principles. In simple terms, convex mirrors bulge outside whereas the concave mirror bulges from inside. 

Tapering figures represent convex mirrors while broadening ones refer to concave mirrors. 

While, both, convex and concave mirrors have different principles, the complexities and comparisons need to be dealt with elaborately. From plane to spherical mirrors, to concave to convex mirrors, the differences attach immense importance to physics students, as well we those who deal with as part of academics as well as profession. 

In this article, we are happy to take you through various aspects of convex mirrors and concave mirrors. We cover: 

Convex  mirror uses 

Concave mirror uses 

Convex mirror examples 

Concave mirror examples 

Characteristics of convex mirrors 

Characteristics of concave mirrors 

Convex mirror diagrams 

Concave mirror diagrams 

Through ray diagram, as well as formula, we will also help you understand the difference between concave mirror and convex mirror, more clearly 

What are Plane Mirror and Spherical Mirror? 

However, before we delve into types of convex mirrors and concave mirrors, let us first talk about the basics of Plane Mirrors and Spherical Mirrors, and how they are different from each other, as well as their applications. 

Plane Mirror 

A plane mirror is a mirror that has a flat and smooth surface, which in turn, always forms a virtual form of the object, with exact shape and size, when it reflects.  Commonly, plane mirrors are those which people generally use in dressing rooms or makeup tables. A plane mirror is known for providing exact image. 

A plane mirror is used for a wide range of applications and purposes that include periscopes and kaleidoscopes, auto industry, mirrors for domestic use, medical especially dental, and torch lights, besides security-related purposes. 

In terms of physics, when light rays hit a plain mirror, the angle of reflection will be the same as the angle of incidence. In plain mirrors, the images are generally laterally inverted, and are erect. The focal length of a plain mirror is counted as infinity. 

Spherical Mirror 

Spherical mirrors are also referred to as curved mirrors, where they have a shape cut out of the spherical surface. Under a spherical mirror, there are two categories: convex mirror and concave mirror. The spherical mirror and its equation hold significant importance in science, owing to its association with optics. 

Unlike plane mirrors, spherical mirrors, both convex mirrors and concave mirrors, have a radius if curvature with a consisting curve, which results in the formation of an image, that can be either virtual or real. 

What is a Concave Mirror? 

A Spherical Mirror that has a reflective surface inside, is called the converging mirror. The main attribute of the concave mirror is that it focuses on pointing the light from the source falling on it, into a single point. And generally, the image formed by these types of mirrors usually varies based on the size, shape, and position of the object. 

Characteristics of Concave Mirror 

The major characteristics of concave mirrors are listed below, 

Converging: A concave mirror is a converging one because, light rays that hit it reflect on the surface, and merge at a particular point. This point is known as a focal point. Concave mirrors allow light to focus to a point. 

Magnification and formation of image: Place a concave mirror close to any object and you will notice that it shows a magnified image that is straight, erect, and of course virtual. The image looks to be larger than the actual size of the object. The concave mirror also looks upright. The reason why concave mirrors feature the formation of virtual images is that the rays that reflect look to diverge from a point located behind the mirror. 

Distance and image properties: In concave mirrors, when the distance between the object and the concave mirror increases, the size of the image decreases. At a particular distance, , the image changes to virtual. Under this circumstance, the true image, in an inverted form manifests on the opposite side of the concave mirror. 

Image formations: concave mirrors create images of different sizes, and diverse in nature, from real to virtual. These features enhance the importance of concave mirrors, which they are widely used in various applications, from domestic to scientific 

Image Formation by Concave Mirror 

The image formed by the concave mirror is either real or virtual and can be small and large based on the position of the sources, and the reflecting point. 

For example, if the distance of the object from the source is large, then it results in real and inverted images. Whereas for the objects placed close to the source, the images formed are erect and virtual. 

Moreover, in this mirror, the light converges at a single point before reflecting, which is referred to as a converging mirror. 

What is a Convex Mirror? 

Convex mirror is also a spherical mirror and is exactly opposite of concave mirrors in its properties. 

Let us first understand convex mirror through its basic definition: 

A convex mirror is a type of spherical mirror that has a reflective surface towards the outside of the bulge, and it is also referred to as diverging mirror. Unlike convex mirrors, in a concave mirror, the light falling on the object diverges as it reflects through the mirror. And generally, as the distance between the source and the object decreases, the size of the image formed increases. 

Characteristics of Convex Mirror 

Diverging: A convex mirror is a standard diverging mirror because when light rays hit the reflecting surface, they diverge or spread. Unlike concave mirrors, convex mirrors cause the light rays to diverge from the definite focal point. 

Types of images – from virtual to diminishing: irrespective of the distance between the object and the convex mirror, the images formed are virtual, uprights, and diminished. The image appears erect and smaller too compared to the actual size of the object. The image also appears on the rear side of the mirror. When you trace it backward, the virtual image forms through the intersection of diverging rays. 

View–Wide: Convex mirrors have an incredible feature to offer a broad canvas of view. This is because they possess an outwardly curved shape, and thus convex mirrors capture a wider area in reflection in comparison with flat and concave mirrors. Due to this, concave mirrors are used whenever there is a need for a larger perspective and a more expansive view. These can be large grounds for parking, sporting, meeting, and intersections, and where security, surveillance, and monitoring are involved 

Image – magnitude, and distance: convex mirrors are known to produce virtual images that are closer to the mirror than the object. The image that is formed by convex mirrors looks diminished and gives an impression of being smaller than the object’s real size. Due to this reduction, in the size of the image, a more expansive area can be captured for reflection.In summary, through convex mirrors, the light diverges as it strikes the reflecting surface The Convex mirrors always result in diminished, erect, and virtual images, regardless of the distance between the mirror and the object. 

Image Formation by convex mirrors and concave mirrors 

As we dwell deeper into the ray incidence on concave and convex mirrors, it becomes easier for us to ascertain and understand the characteristics and behavior of light rays. This is particularly helpful in building precise ray diagrams and analyzing image formation processes. 

Oblique Incidence: When a ray hits the mirror at its pole, its reflection is oblique, forming the same angle as the principal axis. This ensures the angle of incidence is equal to the angle of reflection, thus extending the symmetry of the reflected rays. 

Parallel Incidence: When a ray that is parallel to the principal axis hits the concave mirror or a convex mirror, it takes a definite trajectory. If it is a concave mirror, the ray goes through the focus on the principal axis. If it is for a convex mirror, the reflected ray is born out of the focus on the same side as the incident ray. 

Focus Incidence: When a ray passes through the focus and hits the surface of a concave mirror or a convex mirror, it will be seen traveling parallel to the principal axis. This is the same for both concave and convex mirrors. 

Centre of Curvature Incidence: When a ray travels through the center of curvature of a spherical mirror it will retrace its path after reflection. This is nothing but going through reflection and following the exact similar path in the opposite direction, when the ray touches the centre of the curvature. 

Convex and concave mirrors – important aspects 

Pole: The center point of any spherical mirror from where all measurements are made 

Aperture: An aperture of a mirror is an origin point of reflection of light 

Principal axis: This is an imaginary line passing through the optical center and from the center of curvature of a mirror. Generally, measurements are taken based on this line 

Centre of Curvature: this is a point in the center of the surface of a mirror and goes through the mirror curve, having the same tangent and curvature at the point. 

The radius of Curvature: This is the linear distance between the pole and the center of curvature. 

Principal Focus: This is the Focal Point and is there on the mirror axis. 

Focus: It is a point on the principal axis where light rays parallel to the principal axis come together after reflecting from the mirror. 

As you are aware, many topics such as this in Physics are often complex, and the students often end up struggling to understand these topics and subjects. So, in this process, it is wiser to join an online coaching platform that offers various amazing features for the students to get a better grasp of the subject. One such online tutoring platform is Tutoroot, which offers online interactive classes for students in a personalized, yet effective manner. Enroll with Tutoroot today 

[tutoroot]

What are the Characteristics of Concave and Convex Mirror? 

In Physics, students often encounter the term, spherical mirrors, while learning about how light is deflected and at what angles. Several concepts and chapters are directly derived from it. There are two types of spherical mirrors, Convex Mirrors and Concave Mirrors.

Convex mirrors and concave mirrors differ in their principles. In simple terms, convex mirrors bulge outside whereas the concave mirror bulges from inside.

Tapering figures represent convex mirrors while broadening ones refer to concave mirrors.

While, both, convex and concave mirrors have different principles, the complexities and comparisons need to be dealt with elaborately. From plane to spherical mirrors, to concave to convex mirrors, the differences attach immense importance to physics students, as well we those who deal with as part of academics as well as profession.

We are happy to take you through various aspects of convex mirrors and concave mirrors. We cover:

Convex  mirror uses

Concave mirror uses

Convex mirror examples

Concave mirror examples

Characteristics of convex mirrors

Characteristics of concave mirrors

Convex mirror diagrams

Concave mirror diagrams

Through ray diagram, as well as formula, we will also help you understand the difference between concave mirror and convex mirror, more clearly

What are Plane Mirror and Spherical Mirror?

However, before we delve into types of convex mirrors and concave mirrors, let us first talk about the basics of Plane Mirrors and Spherical Mirrors, and how they are different from each other, as well as their applications.

Plane Mirror

A plane mirror is a mirror that has a flat and smooth surface, which in turn, always forms a virtual form of the object, with exact shape and size, when it reflects.  Commonly, plane mirrors are those which people generally use in dressing rooms or makeup tables. A plane mirror is known for providing exact image.

A plane mirror is used for a wide range of applications and purposes that include periscopes and kaleidoscopes, auto industry, mirrors for domestic use, medical especially dental, and torch lights, besides security-related purposes.

In terms of physics, when light rays hit a plain mirror, the angle of reflection will be the same as the angle of incidence. In plain mirrors, the images are generally laterally inverted, and are erect. The focal length of a plain mirror is counted as infinity.

Spherical Mirror

Spherical mirrors are also referred to as curved mirrors, where they have a shape cut out of the spherical surface. Under a spherical mirror, there are two categories: convex mirror and concave mirror. The spherical mirror and its equation hold significant importance in science, owing to its association with optics.

Unlike plane mirrors, spherical mirrors, both convex mirrors and concave mirrors, have a radius if curvature with a consisting curve, which results in the formation of an image that can be either virtual or real.

A Spherical Mirror that has a reflective surface inside, is called the converging mirror. The main attribute of the concave mirror is that it focuses on pointing the light from the source falling on it, into a single point. And generally, the image formed by these types of mirrors usually varies based on the size, shape, and position of the object.

Characteristics of Concave Mirror

The major characteristics of concave mirrors are listed below,

Converging: A concave mirror is a converging one because, light rays that hit it reflect on the surface, and merge at a particular point. This point is known as a focal point. Concave mirrors allow light to focus to a point.

Magnification and formation of image: Place a concave mirror close to any object and you will notice that it shows a magnified image that is straight, erect, and of course virtual. The image looks to be larger than the actual size of the object. The concave mirror also looks upright. The reason why concave mirrors feature the formation of virtual images is that the rays that reflect look to diverge from a point located behind the mirror.

Distance and image properties: In concave mirrors, when the distance between the object and the concave mirror increases, the size of the image decreases. At a particular distance, , the image changes to virtual. Under this circumstance, the true image, in an inverted form manifests on the opposite side of the concave mirror.

Image formations: concave mirrors create images of different sizes, and diverse in nature, from real to virtual. These features enhance the importance of concave mirrors, which they are widely used in various applications, from domestic to scientific

Convex mirror is also a spherical mirror and is exactly opposite of concave mirrors in its properties.

Let us first understand convex mirror through its basic definition:

A convex mirror is a type of spherical mirror that has a reflective surface towards the outside of the bulge, and it is also referred to as diverging mirror. Unlike convex mirrors, in a concave mirror, the light falling on the object diverges as it reflects through the mirror. And generally, as the distance between the source and the object decreases, the size of the image formed increases.

Characteristics of Convex Mirror

Diverging: A convex mirror is a standard diverging mirror because when light rays hit the reflecting surface, they diverge or spread. Unlike concave mirrors, convex mirrors cause the light rays to diverge from the definite focal point.

Types of images – from virtual to diminishing: irrespective of the distance between the object and the convex mirror, the images formed are virtual, uprights, and diminished. The image appears erect and smaller too compared to the actual size of the object. The image also appears on the rear side of the mirror. When you trace it backward, the virtual image forms through the intersection of diverging rays.

View–Wide: Convex mirrors have an incredible feature to offer a broad canvas of view. This is because they possess an outwardly curved shape, and thus convex mirrors capture a wider area in reflection in comparison with flat and concave mirrors. Due to this, concave mirrors are used whenever there is a need for a larger perspective and a more expansive view. These can be large grounds for parking, sporting, meeting, and intersections, and where security, surveillance, and monitoring are involved

Image – magnitude, and distance: convex mirrors are known to produce virtual images that are closer to the mirror than the object. The image that is formed by convex mirrors looks diminished and gives an impression of being smaller than the object’s real size. Due to this reduction, in the size of the image, a more expansive area can be captured for reflection. In summary, through convex mirrors, the light diverges as it strikes the reflecting surface The Convex mirrors always result in diminished, erect, and virtual images, regardless of the distance between the mirror and the object.

We hope this article cleared the complete information of Ray Diagrams of concave mirrors and ray diagrams for convex mirrors and the differences. Besides, the types of mirrors, use of convex mirrors, use of concave mirrors.

As you are aware, many topics such as this in Physics are often complex, and the students often end up struggling to understand these topics and subjects. So, in this process, it is wiser to join an online coaching platform that offers various amazing features for the students to get a better grasp of the subject. One such online tutoring platform is Tutoroot, which offers online interactive classes for students in a personalised, yet effective manner. Enroll with Tutoroot today.

[arxt1]

Circular orbit of a particle and weak gravitational lensing. (arXiv:2006.13047v1 [gr-qc])

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and time-like particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically non-flat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

from gr-qc updates on arXiv.org https://ift.tt/3g3QNlV

[arxt1]

Curved Space, curved Time, and curved Space-Time in Schwarzschild geodetic geometry. (arXiv:1812.03259v1 [gr-qc])

We investigate geodesic orbits and manifolds for metrics associated with Schwarzschild geometry, considering space and time curvatures separately. For `a-temporal' space, we solve a central geodesic orbit equation in terms of elliptic integrals. The intrinsic geometry of a two-sided equatorial plane corresponds to that of a full Flamm's paraboloid. Two kinds of geodesics emerge. Both kinds may or may not encircle the hole region any number of times, crossing themselves correspondingly. Regular geodesics reach a periastron greater than the $r_S$ Schwarzschild radius, thus remaining confined to a half of Flamm's paraboloid. Singular or $s$-geodesics tangentially reach the $r_S$ circle. These $s$-geodesics must then be regarded as funneling through the `belt' of the full Flamm's paraboloid. Infinitely many geodesics can possibly be drawn between any two points, but they must be of specific regular or singular types. A precise classification can be made in terms of impact parameters. Geodesic structure and completeness is conveyed by computer-generated figures depicting either Schwarzschild equatorial plane or Flamm's paraboloid. For the `curved-time' metric, devoid of any spatial curvature, geodesic orbits have the same apsides as in Schwarzschild space-time. We focus on null geodesics in particular. For the limit of light grazing the sun, asymptotic `spatial bending' and `time bending' become essentially equal, adding up to the total light deflection of 1.75 arc-seconds predicted by general relativity. However, for a much closer approach of the periastron to $r_S$, `time bending' largely exceeds `spatial bending' of light, while their sum remains substantially below that of Schwarzschild space-time.

from gr-qc updates on arXiv.org https://ift.tt/2QqGwrw