Purpose: To verify Snell's law of refraction. To measure the index of refraction of water.

Discussion: The speed of light travelling in a perfect vacuum is c = 3.0 * 10⁸ m/s. When light travels in some material it's speed, v, is slightly less. The index of refraction of a material is n = c/v, which is always greater than 1. Snell's law of refraction states that in passing from one material to another the path of the light is refracted at the boundary according to the equation

q_i and q_r are the incident and refracted angles, respectively, and n_iand n_r are the respective indices of refraction of the two materials. This refraction creates a shift in the apparent position of an object when light from it must pass through different materials before reaching the observer's eye. In this experiment, q_iis in the water, and q_r is in the air. For the purposes of this experiment, we can use 1 for the index of refraction of air (it is only very slightly greater). The presence of the glass at the boundary has a relatively small effect due to the small thickness of the glass in comparison to the thickness of the water.

Procedure:
1. Fill the tank half full of water. Make sure that the scratch on the glass is directly above the screw holding the moveable arm.

2. Place the moveable arm at 5°. Look at the scratch on the glass through the slit in the moveable arm. Slide the moveable slit along the back of the tray until the two slits and the scratch are in line when you look through the air in the tray. It is easier to see the moveable slit if it is against a white background. You have just made q_i= 5°. (Think about this for a minute before going any further.)

3. Rotate the arm until the two slits and the scratch are in line when you look through the water in the tray. You are now measuring q_r. Read q_r to the nearest tenth of a degree from the scale. Note that the scale is marked in increments of 0.25° , i. e. fourths of a degree.

4. Repeat steps 2 and 3 as you increase q_i in steps of 5°. You cannot make q_i much bigger than about 45°, because of total internal reflection in the water, and the difficulty in seeing the moveable slit when q_r is large. You may want to repeat some of your first measurements after you are accustomed to the measurement technique. Also notice that q_r = 0° when q_i = 0°, so this should be used as a data point for your graph.

5. Make a graph of sin q_r vs. sin q_i. If your data fits reasonably well on a straight line, you have verified Snell's law. Find the slope of your best line. This slope should correspond to the index of refraction of water, which is known to be 1.33.

6. Calculate the percentage error.

7. What are the greatest sources of experimental error? Be specific.