# Index of Refraction

#### Purpose

To determine the index of refraction of unknown plastic material.

#### Objectives

• To see how measuring small values leads to larger inaccuracy in the final results

#### Equipment

• Light source, rectangular prism of unknown material
• Paper, protractor

#### Theory

The angles at which light refracts as it crosses from one medium to another is determined by Snells Law

$n_1 \sin \Theta_1 = n_2 \sin \Theta_2$

Here n1 and n2 are the index of refraction of the material infront and behind the boundary surface, and Θ1 and Θ2 are the angles of incidence and refraction, respectively.

#### Experimental Setup

Place the rectangular prism on a blank piece of paper and outline its location. Using the light source, trace a beam of light as it enters the prism and as it exits back into air after it.

The second to the last picture in this manual shows how the setup looks.

#### Experimental Activity

Using the prism outline and the beams of light traces on the paper sheet, draw the angle of refraction in the plastic prism.

Measure the angle of incidence and refraction. Determine the index of refraction.

Note. You can set up the incident angle to have any value between 0 and 90o. Repeat the measurement for the following values of the incident angle:

Incident Angle in Degree Refracted Angle in Degree Index of Refraction, n
10
20
30
40
50

#### Questions and Assignments

1. Do you have similar values for the index of refraction of the prism, or do they differ?
2. If the value for the index of refraction are different, which value is the correct one? Should you take the smallest value? The largest value? The average?
3. Your measurements have different experimental error. Your measurements for the larger angles are more accurate than those for the smaller angles. Do you know why?