steam2017lazermaze-blog

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Laser Maze Chalenge

Measurements:

Angle of Incidence = 35º

Angle of Refraction = 24.6º

Refraction Index = 1.377

Mirror #1: Angle of Incidence = 44º

Mirror #1: Angle of reflection = 44º

Mirror #2: Angle of Incidence = 50º

Mirror #2: Angle of Reflection = 50º

Prism: Angle of Incidence= 19º

Prism: Angle of Refraction = 9.8º

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Overall:

To sum up, this experiment was a success as we were able to hit the target with the laser. Although we weren’t successful in the first trial, after some adjustments, we were able to come up with solutions that eventually helped us accomplish this challenge.

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Plastic Prism

Finally, the last stage of this challenge was to move through a plastic prism, which would then hit a target. For this stage, we applied the concept from investigation #1 by first finding the angle of incidence, which was 19º. Then, we input this angle value to the equation given by the graph in order to calculate the angle of refraction, which was 9.8º. Similar to the salt concentration, by finding these angles, we were able to determine where the laser would end up. After few trials and adjustments, the laser was able to hit the target.

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Mirrors:

Next, after going through the tank, the laser had to move to the mirrors. In this stage, we applied the concept learn through investigation #3, which states that the angle of incidence that goes through a mirror is equal to its angle of reflection. By drawing another normal line in the mirror, the angle of incidence was 44º. Thus, the angle of reflection was supposed to also be 44º. We then applied the same concept for the next mirror.

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Salt Concentration

For the first task attempting the laser maze challenge, we were given a laser and a tank with 13% salt concentration in fixed position. Therefore, we had to figure out where the laser was going to end up through the salt water concentration. We applied the concept of drawing a normal line and measure the angle of incidence, which was 35º. Based on the 2nd investigation, we used our equation that determines the refraction index in order to find the angle of refraction, which was 24.6º. In the end, from those two measurements, we could find where the laser would end up.

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Glass Reflection Graph and Table Showing the Relationship Between the Angle of Incidence and the Angle of Reflection 

In conclusion, we discovered that both the angle of incidence and the angle of reflection are equal, therefore having a symmetrical angle of incidence and reflection

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Day 2

Investigation Number 3: Mirror Reflection

In this investigation we had to find the relationship between the angle of incidence (laser striking the mirror) and the angle of reflection. 

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Conclusion

Conclusion:

     The purpose of this investigation was to find the relationship between the salt concentration(%) on the Index of Refraction. The hypothesis of this experiment was: if the salt concentration increases, then the index of refraction will decrease because as the water gets denser, it increases the angle of refraction. Since the index of refraction equals to the Sin of incidence divided by sin of angle of refraction, the value becomes smaller. According to the data, it does not support the hypothesis because as our salt concentration went from 0% to 1% until 2.5%, the x cm got bigger, increasing the refraction index. However, part of the data became accurate when the salt concentration went to 5%, which caused the x cm decrease, making the refraction index be bigger. For example, the x cm for 1% was 9.50 cm, making the refraction index 1.35. The x cm for 2.5 was 9.90 cm, making the refraction index 1.31. For the 5% salt water concentration, the x cm was 9.00, making the cm from the previous trial .90 cm shorter, in result making the refraction index 1.40. In the 10% salt concentration, the x cm went up to 9.70, but still making the distance shorter than it was in the 2.5%, making the refractive index 1.33.

     Even though, the data suggest that the hypothesis is wrong, according to the accepted model, the hypothesis is right. The relationship between the salt concentration and the refraction index is that there are directly proportional. If the salt concentration increases, the refractive index increases.When the water becomes more dense, the light will bend more towards the normal. Thus, decreasing the angle of refraction. The sine of a smaller angle from 0º to 90º will give a lower value, therefore when calculating the Refraction Index, the value becomes larger.

Evaluation:

     After doing investigacion ll we noticed a couple of limitations, and found how these issues could be mitigated. One random error was that in the 5% salt concentration, a piece of paper fell inside the tank, by having to take it out, someone had to take it out, having contact with the water in the tank. The effect of these limitation was that it might’ve changed the ph or the chemicals inside the water, slightly affecting the data. This issue can be prevented by being careful of our surroundings. A systematic limitation is that putting the tank of water and pins in the same place 5 times it’s near impossible. This could affect the final result by giving us a close by not exact difference of the angle that came out of the water. Though this can’t be solved we could have kept the first two pins on the same place to decrease the amount of limitations. Additionally, we could have more trials for each concentration in order to have more data, making this reliable. Also, another systematic limitation is that it's near impossible to know exactly where the pin is gonna be reflected through the water. Again this could affect our data by giving us a close but not exact result. A solution for this is to have more data and trials to make this credible and reliable. 

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Data Analysis

Calculations:

Angle of refraction:

0%: -1tan (9.3/15.4)= 31.13°

1%: -1tan (9.5/15.4)= 31.67°

2.5%: -1tan (9.9/15.4)= 32.74°

5%: -1tan (9.0/15.4)= 30.30°

10%: -1tan (9.7/15.4)= 32.21°

Refraction Index:

0%: sin(45)/sin(31.13)= 1.37

1%: sin(45)/sin(31.67)= 1.35

2.5%: sin(45)/sin(32.74)= 1.31

5%: sin(45)/sin(30.30)= 1.40

10%: sin(45)/sin(32.21)= 1.33

Analysis of Graph

Our correlation is -16%, meaning that the data is not correct

The data does not show a pattern between each salt concentration

The data is supposed to be directly proportional

As a result, the slope is supposed to be positive

When the salt concentration increases, the refractive index increases

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Tables

Image 1. Example of a trial 

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Introduction

Research Question:

What is the relationship between the salt concentration and the Index of refraction?

Hypothesis:

If the salt concentration increases, then the index of refraction will increase because as the water gets denser, it decreases the angle of refraction. Since the index of refraction equals to the Sin of incidence divided by sin of angle of refraction, the value becomes larger.

IV: Concentration of Salt (%)

DV: Index of Refractions

Control Variables:

Same amount of liquid (1 liter) must be used throughout the experiment, otherwise the salt will be more or less concentrated in the different trials.

Same sized container must be used throughout the experiment. If the water reaches different levels of the glass container during each trial, the data could be affected.

Same angle of incidence must be used throughout the experiment, otherwise we would be left with results that do not make sense (outliers).

Same type of salt because some may be more pure or have a greater density than others. Furthermore, different types of salt may be thicker than others.

Same type of water used throughout experiment (tap water) as bottled water may have different chemicals inside which could affect the density.

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Day 1

Investigation 2: The Relationship Between the Salt Concentration and the Index of Refraction

Key:

0% = No salt = 1000ml of Water

1% = 10 grams of salt  = 50ml of salt water + 875ml of water

2.5% = 25 grams of salt = 125ml of salt water + 875 ml of water

5% = 50 grams of salt = 250 ml of salt water + 750 ml of water

10% = 100 grams of salt = 500ml of Water + 500ml of salt water

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Table and Graph Showing the Index of Refraction of a Transparent Block

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The 5 trials we completed in order to find the refraction of a transparent block with 5 different degrees as seen in the pictures

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Day 1:

Objective: 

Through a series of investigations we will find the ideal path our laser will take to reach the target, while going through several obstacles. 

Investigation 1: Index of Refraction of a Transparent Block 

Collected 5 data points using the following key to find the index of refraction:                                                 

-Angle of refraction: (Inverse tan x/ y)

-Refraction Index: (Sin of incidence/ sin of angle of refraction)

-Angle of incidence: Starting angle

-X=Distance from starting angle to the final one

-Y=Width