6.2 Refraction

The velocity of light in free space is very close to  cm/s; moreover, the velocity is the same for all wavelengths. The situation is different in most material substances. With few exceptions, the velocity of light in material substances is less than the velocity in free space. Not only is the velocity less, it varies with the wavelength of the light passing through the medium.

If light travels through two media with different velocities, the wave nature of the light causes its direction to be altered as it passes from one medium into the other. This phenomenon is referred to as refraction. We can define the index of refraction (n) of a material to be the ratio of the velocity of light in free space (c) to its velocity in the given material (v). Since the velocity (v) varies with wavelength, we must specify the corresponding wavelength when referring to an index of refraction.

The purpose of this portion of the experiment is to determine the relation between the direction of the incident ray, the direction of the refracted ray, and the index of refraction. The index of glass (for example) varies by less than 2% throughout the visible spectrum. Therefore, using the incandescent light source (rather than a single frequency laser source) doesn't introduce much error.

6.2.1 Index of Refraction

1. Take a square piece of millimeter graph paper about 5 cm on a side. Place the paper between the glass plate and the special component carrier on the angular translator. The magnetic surface will hold the glass plate and paper in place.
2. Adjust the position of the special component carrier until the back surface of the glass plate coincides with the perpendicularly scored line on the table.
3. With the glass plate sitting perpendicular to the bench, adjust the position of the aperture mask so that one vertical edge of the image on the paper lines up with the scored line on the table which is parallel to the bench. If the glass does not alter the lights's path, the vertical edge which was centered should remain centered although the translator's table is rotated.
4. Rotate the table and record what happens to the previously centered edge. Is the incident ray refracted toward or away from the normal to the glass? Before arriving for the experiment, work out how to calculate the index of refraction given the angle of rotation and the edge displacement of the image using the quantities shown in Fig. D.

   Note: Using this method, a small error is introduced since we are not certain that the light very near to the image's edge was exactly perpendicular to the glass plate in the beginning. (Why?) Hence the measured value of (as shown in Fig. D is not accurate. The method in the following section gives more accurate results.

     
   
   Figure D: Calculating the index of refraction.
   

5. Remove the paper from between the glass plate and component carrier. With the glass place perpendicular to the bench, put the viewing screen directly behind the plate and adjust the aperture mask to center the image on the screen. Rotate the table to a convenient angle. Light is refracted toward the normal when passing from air to glass. Is the same true when light propagates from glass to air? By observing the position of the image on the viewing screen, you can see that the refraction must be away from the normal at a glass-air interface (see Figure E).

     
   
   Figure E: Index of refraction: improved method.
   

6.2.2 Critical Angles

1. Remove the special component carrier from the angular translator table and replace it with the prism.
2. With the scored lines running perpendicular and parallel to the bench, position the prism so that one of the small faces is centered on the table and coincides with the perpendicularly scored line.
3. Check the position of the aperture mask so that the center of the light beam travels directly over the center of the table and parallel to the bench.
4. Move the arm until the refracted beam is imaged on the viewing screen. Now rotate the table and watch the movement of the image (move the arm if necessary). Although the prism is continually rotated in the same direction, note that the image moves in one direction and then begins moving in the other direction. The point where the image reverses direction coincides with the angle of minimum deviation. That is, at that particular angle of incidence the light beam is deviated least from its original path.
5. From the angle of minimum deviation, calculate the index of refraction of the prism material. Before coming to the lab, work out how to find the index of refraction from the measured minimum deviation angle.

   Note: The edges of the image are colored. Why? This phenomenon is called dispersion.

6. Rotate the table until the refracted beam is parallel to the large surface (slanted surface) of the prism. In this position, no light propagates through the slanted surface; all of the light is internally reflected.
7. Knowing the angle of incidence we can calculate the angle of incidence of the light in the prism as it reaches the slanted surface. The angle is called the critical angle.
8. The prism is designed so that any light normal to the slanted surface is totally internally reflected. Position the prism to observe this phenomenon.