# Index of Refraction

Goal: To determine the index of refraction of different media
• Theory:
Light travels at different speeds in different media. Each medium is characterized by an index of refraction defined as:

where c is the speed of light in free space, and v is the speed in that particular medium. When light reaches the interface between two media, its direction is changed according to Snell's Law:

Here, n1 and &theta1 refer to the index of refraction and the angle between the direction of light and the normal to the interface in the medium in front, and n2 and &theta2 to those in the medium behind the interface as shown on the diagram 1.

If the index of refraction of the first medium is known, the Snell's Law provides a way to determine the index of refraction of an unknown medium by simply measuring the two angles. Thus, the index of the second medium will be equal to:

• Preliminary Setup:
• You need:
• Two objects:
• Transparent rectangular container with relatively thin walls
• Transparent rectangular cube
• Blank sheet of paper and two pencils,
• Protractor.

• Activity 1: Determine the index of refraction of tap water.

• Experiment:  On a blank sheet of paper, draw a horizontal straight line, and a second line at an angle &theta . See the value for theta in the data table below. The intersection point of the two lines is where the light crosses from air into the container. Fill the container with tap water and place it so that its length is aligned with the horizontal line. Outline its contour. Hold the first pencil along the second line and look at it through the water keeping one eye closed. With the second pencil, mark the line that connects your eye to the first pencil (beyond the water container). Once you have drawn the line of sight, remove the water container and extend the line to where it reaches the edge of the container. The intersection point of the container edge and the line of sight is the point where the light exits the container back into air. Connect the points where the light enters and exits the container. Measure the angle in water between the the light and the edge of the water container, &phi Calculate the index of refraction. Note: You must use (90-&theta) and (90-&phi) as the angles in Snell's Law. Repeat the procedure for two more values of &theta
• Data table:

 &theta &phi nwater 35o 40o 45o
 &theta &phi nwater

• Results.
• Average value for nwater:__________
• What is the percent difference between your value and the value usually reported in textbooks, nw=1.33? Answer:____________
• If your percent difference is more than 5%, you must go back and re-do the experiment for more angles &theta . Write down your data in Table 2.
• Activity 2: Determine the index of refraction of an unknown transparent object.

• Experiment: Repeat the procedure outlined in Activity 1, only this time using the cube instead of the water container.
• Data table:

 &theta &phi ncube 35o 40o 45o

• Results.
• Average value for ncube:__________