Reflection and Refraction of Light

Overview

Light bends when it enters from one medium to another. This bending of light is called Refraction of light. The relationship between the angle of incidence (medium 1) and the angle of refraction (in the medium 2) is given by Snell’s Law:

 Where n₁ is the index of refraction, q ₁ angle of incidence in medium 1;  n₂ is the index of refraction, q ₂ angle of refraction in medium 2. The angles, q  are measured with respect to the normal to the surface between the two medium. When light travels from an optically light medium to an optically dense medium, i.e. n₁< n₂, then light bends towards the normal after refraction. Index of refraction of a material is defined as the ratio of speed of light in the vacuum (c) and the speed of light in the material (v) :  n = c/v . The value of n ≥ 1.

In this lab you will do simulation on bending of light as it passes through different media. You will learn about total internal reflection and dispersion of light as it passes through a prism.

Read Ch. 22, Sec 2 – 4, 7 for concepts.

Simulation:  Open Bending Light

http://phet.colorado.edu/sims/html/bending-light/latest/bending-light_en.html

Take few minutes to familiarize yourself with the simulation. You will be able to switch between Intro, Prisms and More Tools.

1. Finding Index of Refraction from Snell’s Law

1. Click on “More Tools” tab.    You should see a light source and two mediums separated by a boundary. You can change the index of refraction of each medium by moving the sliding switch. Make sure that the “Normal” and the “angle” are checked. You can change the angle of incidence of light in medium 1 by pressing on the source and sliding it. Notice that you will also see a reflected light when light is incident on a boundary with two different values of n.

2. You will measure the angle q ₁ between the incident light and the normal in medium 1 (above the surface) and q ₂ between refracting light and the normal in medium 2 (below the surface). Use the red light (670 nm) for this experiment.

3.  Change the incident and refracting medium for different angle of incidence and complete the table below. Note: You may have a hard time in setting the exact angle. It is acceptable to have an angle within ±0.5°. Write down the angle you used.

Table 9.1: Angle of refraction for different material combination.

Set angle of incidence to about , q₁ = 30°.  Actual angle used:  _________

From the data of this table. Answer the following:

i.          When n₁ = n₂:  Refracted light bends toward/bends away/does not deflect.

ii.         When n₁ < n₂:  Refracted light bends toward/bends away/does not deflect.

iii.        When n₁> n₂:  Refracted light bends toward/bends away/does not deflect.

4. Set Medium 1 = Air, water and Glass; Medium 2 = Mystery A.  Complete the following table. Calculate the Index of Refraction of the mystery medium using Snell’s Law (Eq. 9.1). Look up the textbook or internet to find a possible material for the mystery medium from the value n₂.

Table 9.2A: Index of refraction of an unknown medium. Set Medium 2 = Mystery A

5.   Set Medium 1 = Air, water and Glass; Medium 2 = mystery B.  Complete the following table. Calculate the Index of Refraction of the mystery medium using Snell’s Law (Eq. 9.1). Look up the textbook or internet to find a possible material for the mystery medium from the value n₂.

Table 9.2B: Index of refraction of an unknown medium. Set Medium 2 = Mystery B

6.  Another way to find the index of refraction of the Mystery Medium B:  Set the incident angle, q₁ = 30° and index of refraction, n₁ = Mystery B. Start with medium 2, index of refraction n₂  = 1 (Air). You should see two rays: (i) reflected light and (ii) refracted light. Keeping the angle constant (q₁=30°), slide the Medium 2 index of refraction, n₂. At some value of n₂, you will see that the reflected light will disappear. Continue to slide the Medium 2 index of refraction. For a certain value of n₂, light will travel between the boundaries un-deflected, i.e. q₂  = 30°. This happens when the two medium are optically same; i.e. n₁ = n₂ = n.

Mystery Medium B, n = _______________      Medium material is ________________

2. Speed of Light in Different Medium

Light travels at different speed when it travels in different medium. The speed of light is c = 2.997 x 10⁸ m/s » 3.0 x 10⁸ m/s in vacuum. This is true for all the color (frequency) of light. For this part of the lab, you will measure (i) the speed of light in different media; (ii) the speed of light as a function of color in a medium.

1. Set Medium 1 = Air; Medium 2 = Water.  Set the source to any arbitrary angle and turn it ON. Grab the speed meter   and place the pointed tip on top of the light ray. You should see an arrow pop up (in the direction of ray) and the meter will give a reading of the speed in terms of c. You can calculate the index of refraction of the medium from n = c/v.   Complete the table below. The angle doesn’t matter. You can set it to any arbitrary angle.

Table 9.3: Speed of light in different medium

Light bends by different amount for different color of light. Note that each color of light has different wavelength and frequency. You can check the “Angle” box at the lower left corner to determine the angle.

Table 9.4: Speed of light as function of color. Set Medium 1 = Air; Medium 2 =Custom 1.570, Angle q₁ = 30°  ;

2. You will find in the above Table that the speed of light (measured by Speed Meter) hardly changes, while the index of refraction varies between 1.569 to 1.592. Why do you think the speed of light measured using the Speed Meter doesn’t reflect this change? Explain.

3. Dispersion of Light with Prism

White light consists of different colors of light. Different color of light bends by different amount when it passes from one medium to another. This is due to a slight variation of index of refraction of different color of light as it passes through a medium. As a result, we see a spreading of different color (rainbow). This spreading of light is called Dispersion.

Select the tab, “Prism”   for this part of the simulation. Select the triangular prism and white light.  Change the angle of incidence until you see the component lights (Red, Green, Yellow, Blue) separated by the prism. You can move the light source as well as the prism to get the best spreading. Take a screenshot of the diagram and attach it here.

4. Total Internal Reflection and Critical Angle

When light is incident from an optically dense medium to a light medium, i.e. n₁ > n₂, the refracted light bends away from the normal. For a certain angle of incidence (called the critical angle, q_c) the refracted ray will be 90° from the normal. If the angle of incidence is any larger, the ray is totally reflected in medium 1 and no light comes out of medium 2. This is called Total Internal Reflection.

For this part of the lab, you will find the critical angle for different sets of boundaries. Select “More Tools” tab.  

1. Set the Medium 1 = Glass (n₁ = 1.5);  Medium 2 = Air ( n₂ = 1.0).

2. Start with q₁ = 0. Gradually increase q₁ until the refracted ray,  q₂ = 90° . This is incident angle is the critical angle, q_c . If you keep on increasing q₁, there will only be reflected light. In this way, you can figure out the critical angle for different mediums at the boundaries listed in the table below.     

Table 9.5: Critical angle of different sets of boundaries

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