PC1222 Fundamentals of Physics II Reflection and Refraction of Light 1 Objectives Investigate for reflection of rays from a plane surface, the dependence of the angle of reflection on the angle of incidence. Investigate refraction of rays from air into a transparent plastic medium and from the transparent plastic medium into air. Determine the index of refraction of a plastic medium from direct measurement of angles of incidence and refraction of a light ray. Investigate dispersion of light and total internal reflection when light rays travel from plastic medium into air. 2 Equipment List Light source Ray table D-shaped lens 3 Theory Light is an electromagnetic wave. The theory of the propagation of light and its interactions with matter is by no means trivial; nevertheless, it is possible to understand most of the fundamental features of optical instruments such as eyeglasses, cameras, microscopes, telescopes, etc. through a simple theory based on the idealized concept of a light ray. A light ray is a thin pencil of light that travels along a straight line until it encounters matter, at which point it is reflected, refracted or absorbed. The thin red beam from a laser pointer is a good approximation of such a ray. When light strikes the surface of a material, some light is usually reflected. The reflection of light rays from a plane surface such as a glass plate or a plane mirror is described by the law of reflection, which states that the angle of incidence θ i is equal to the angle of reflection θ r. These angles are measured from a line perpendicular or normal to the reflecting surface at the point of incidence (see Figure 1). Also, the incident and reflected rays and the normal lie in the same plane. Page 1 of 6
Reflection and Refraction of Light Page 2 of 6 Figure 1: Refraction of light (n 1 < n 2 ). Figure 2: Refraction of light (n 1 > n 2 ). In general, light rays incident on a plane interface will be partially reflected and partially transmitted into the second medium. The transmitted ray undergoes a change in direction because the speed of light is different for different media. The ray is said to be refracted (see Figure 2). The angle of incidence is θ 1 and the angle of refraction is θ 2. These angles are measured from the normal to the plane interface at the point of incidence. The speed of light in vacuum is c ( 3.00 10 8 m/s), the maximum possible speed of light. For any medium, the speed of light is v where v c. A quantity called the index of refraction n for any medium is defined by n = c (1) v The only allowed value of n are n 1 as v c. The relationship between the angle of incidence θ 1 and the refracted angle θ 2 is known as Snell s law: n 1 sin θ 1 = n 2 sin θ 2 (2) For a vacuum, n = 1, the index of refraction of air is approximately unity and all other materials have n > 1. For water, n = 1.33. The index of refraction also depends on the wavelength,or colour, of the light. Therefore, light rays of different wavelength (colour) have different angles of refraction (θ 2 ) for identical angles of incidence (θ 1 ). The wavelength dependence of a material s index of refraction is known as dispersion. We see from (1) that the index of refraction is a measure of speed of light in a transparent material, or a measure of what is called the optical density of a material. For example, the speed of light in water is less than that in air, so water is said to have a greater optical density than air. Thus, the greater the index of refraction, the greater its optical density and the lesser the speed of light in the material.
Reflection and Refraction of Light Page 3 of 6 In terms of the indices of refraction and Snell s law, we have the following relationships for refraction: If the second medium is less optically dense than the first medium (n 2 refracted ray is bent away from the normal (θ 2 > θ 1 ) as in Figure 2. < n 1 ), the If the second medium is more optically dense than the first medium (n 2 > n 1 ), the refracted ray is bent toward the normal (θ 2 < θ 1 ), as for reverse ray tracing in Figure 2. Figure 3: Total internal reflection. For light ray incidents on a boundary from a denser medium (see Figure 3), Snell s law indicates that there is a certain angle of incidence θ 1 for which the angle of refraction will be θ 2 = 90. This angle of incidence is known as the critical angle θ c. If the angle of incidence larger than the critical angle, i.e. θ 1 > θ c, there will be no refracted ray and the incident ray will exhibit a total internal reflection from the boundary into the denser medium. For this special case, Snell s law states n 1 sin θ c = n 2 sin 90 (3) Solving for the sine of critical angle gives: sin θ c = n 2 n 1 (4)
Reflection and Refraction of Light Page 4 of 6 4 Laboratory Work Part A: Law of Reflections In this part of the experiment, you will determine the relationship between the angle of incidence and the angle of refraction for light passing from air into a more optically dense medium (the acrylic of the D-shaped lens). A-1. Place the light source in ray-box mode on the table. Turn the wheel to select a single ray. A-2. Put the ray table in front of the light source so the single ray from the light source crosses the exact center of the ray table as in Figure 4. Figure 4: Initial setup. A-3. Put the D-shaped lens on the ray table exactly centered in the marked outline. A-4. Rotate the ray table so the ray enters the lens through the flat surface and the angle of incidence is 0. A-5. Vary the angle of incidence θ i by rotating the ray table until you clearly see the incident and reflected rays. A-6. Measure the angle of incidence θ i and the angle of reflection θ m. Record their values in Data Table 1. Note: Since the incident beam of light has a finite width, the same edge of the beam should be used to set the incident angle θ i and to measure the reflected angle θ r. Make sure that this edge of the beam passes through the center point of the ray table, otherwise your measurements of angles will be incorrect. A-7. Repeat the above procedures to complete Data Table 1 with three different angles of incidence.
Reflection and Refraction of Light Page 5 of 6 Part B: Snell s Law In Trial 1 of this part of the experiment, you will determine the relationship between the angle of incidence and the angle of refraction for light passing from air into a more optically dense medium (the acrylic of the D-shaped lens). In Trial 2 of this part of the experiment, you will determine whether the same relationship (Snell s law) holds between the angles of incidence and refraction for light passing out of a more optically dense medium back into air. B-1. Turn the ray table so the incoming ray enters the lens through the flat surface (see Figure 5). Figure 5: Refraction of light passing into the lens (Trial 1) and out of the lens (Trial 2). B-2. Vary the angle of incidence θ 1 by rotating the ray table, in 10 increments from 10 to 80. For each angle of incidence (θ 1 ), observe the corresponding angle of refraction (θ 2 ) and record it in Data Table 2. Note: Since the incident beam of light has a finite width, the same edge of the beam should be used to set the incident angle θ 1 and to measure the refracted angle θ 2. Make sure that this edge of the beam passes through the center point of the ray table, otherwise your measurements of angles will be incorrect. B-3. Turn the ray table so the incoming ray enters the lens through the curved surface (see Figure 5). Note: Make sure that you use the side of the beam that is closer to the normal as your reference edge and that this edge goes through the center point of the ray table. The angle of incidence θ 3 is now measured inside the lens while the angle of refraction θ 4 is outside. B-4. Vary the angle of incidence θ 3 by rotating the ray table, in 5 increments from 5 to 40. For each angle of incidence (θ 3 ), observe the corresponding angle of refraction (θ 4 ) and record it in Data Table 3.
Reflection and Refraction of Light Page 6 of 6 Part C: Dispersion of Light In this part of the experiment, you will determine the index of refraction of acrylic at two different wavelengths (colours). The wavelength dependence of a material s index of refraction is known as dispersion. C-1. Turn the ray table so the ray enters the lens through the curved surface and the angle of incidence is 0. C-2. Hold a piece of white paper vertically near the edge of the ray table so the outgoing ray is visible on the paper. C-3. Slowly rotate the ray table to increase the angle of incidence. Notice that the ray is refracted only at the flat surface of the lens, not at the curved surface. As you continue to increase the angle of incidence, observe the refracted light on the paper. Record the angle of incidence as θ min in Data Table 4 when you begin to notice colour separation in the refracted light. Record the angle of incidence as θ max in Data Table 4 when the maximum colour separation occurs. C-4. Set the angle of incidence at one of the angles between θ min and θ max by rotating the ray table. Record this angle as θ in Data Table 4. For this angle of incidence θ, observe the corresponding angle of refraction for red light (θ red ) and blue light (θ blue ) respectively. Record these angles in Data Table 4. Part D: Total Internal Reflection In this part of the experiment, you will determine the critical angle at which total internal reflection occurs in the acrylic of the D-shaped lens and confirm your result using Snell s law. D-1. Turn the ray table so the ray enters the lens through the curved surface and the angle of incidence is 0. D-2. Slowly rotate the ray table to increase the angle of incidence until the emerging ray (red light) just barely disappears. Record the angle of incidence as θ c,red in Data Table 5. D-3. Adjust the angle of incidence until the emerging ray (blue light) just barely disappears. Record this angle of incidence as θ c,blue in Data Table 5. Last updated: Tuesday 13 th January, 2009 5:30pm (KHCM)