Exercise 1: Designing the experiment

Physics 1A03 Team

Exercise 1: Designing the experiment

Like in previous experiments, your task is to measure a parameter that may seem difficult to measure. The index of refraction describes the speed of light through a medium, but you won’t be able to measure displacement over time like in Lab 1 (light is waaaaay faster than your camera’s frame rate… unless you have this camera). Since you can’t measure the speed of light in various media directly you will make measurements based on Snell’s Law and determine the index of refraction indirectly. You will work out how to do this below.

Snell’s Law is a great equation; two sides, 4 variables, one sweet sweet principle. That means, in order to solve for the index of refraction of n₂, you need to know θ_inc , θ_ref , and n₁. To get familiar with this great equation, consider the following chart of experimental data:

θ_inc [deg]	θ_ref [deg]	sin(θ_inc) [1]	sin(θ_ref) [1]
10	12.5
20	25.1
30	38.4
40	53.0
50	72.0

Chart download

The experiment was set up exactly like the picture of Physics Girl spearfishing (light travels from the first material into a second material at angle θ_inc, and is refracted at an angle θ_ref as it travels through the second material) with one difference: the materials are not air and water, and their refractive indices are unknown. However, this data can be used to determine the ratio between the two material’s refractive indices (n₁/n₂). In the next section, you will do exactly that.

Exercise 1.1 (1 mark)

Calculate sin(θ_ref) and sin(θ_inc) for the values in the table above, and submit your table.

Exercise 1.2 (1 mark)

Referring to Snell’s Law, which material do you think has the higher refractive index; the first material (incident angle), or the second material (refracted angle)? Choose the correct answer on Crowdmark.

a. The first material has a higher refractive index since $\sin{(\theta_{ref})} < \sin{(\theta_{inc})}$ therefore $n_{inc} > n_{ref}$

b. The first material has a higher refractive index since $\sin{(\theta_{ref})} > \sin{(\theta_{inc})}$ therefore $n_{inc} > n_{ref}$

c. The second material has a higher refractive index since $\sin{(\theta_{ref})} < \sin{(\theta_{inc})}$ therefore $n_{ref} > n_{inc}$

d. The second material has a higher refractive index since $\sin{(\theta_{ref})} > \sin{(\theta_{inc})}$ therefore $n_{ref} > n_{inc}$

Exercise 1.3 (3 marks)

i) Create a plot of sin(θ_ref) vs sin(θ_inc) from your table (Hint: remember that this means that sin(θ_ref) is on the y-axis).

ii) Draw and calculate a line of best fit. Show the equation of the line of best fit on your plot. iii) Use your line of best fit to calculate n₁/n₂. iv) If n₂ = 1.33, what is n₁?

Exercise 1.4 (2 marks)

If you extend your line of best fit you will see that the line goes through the point of sin(θ_ref) =1. i) What is the refracted angle at this point? ii) What is the incident angle?

a. i) $\theta_{ref} = 90^\circ$ ii) $\theta_{inc} = 1.24^\circ$

b. i) $\theta_{ref} = 1.24^\circ$ ii) $\theta_{inc} = 90^\circ$

c. i) $\theta_{ref} = 90^\circ$ ii) $\theta_{inc} = 53.6^\circ$

d. i) $\theta_{ref} = 53.6^\circ$ ii) $\theta_{inc} = 90^\circ$

Exercise 1.5 (1 mark)

If you continue to increase theta_inc, what happens to sin(θ_ref)? (Hint: can you have sin(θ_ref) > 1?) This is called Total Internal Reflection, and an important concept in designing optical fibers

In the next exercises, you will perform an experiment and use Snell’s Law to determine the index of refraction of water.

Before you continue!

Before continuing, be sure you have completed (1.1) to (1.3), which will be graded and submitted through Crowdmark.

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Physics 1A03 - Laboratory Experiments Copyright © by Physics 1A03 Team is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, except where otherwise noted.