# The Refraction of Light

## Questions:

1. When light refracts when passing from one medium to another, how is the angle of incidence related to the angle of refraction?
2. Does light refract at different angles in different substances?

## Discussion:

You know that light, when passing from one medium to another, will refract or bend. It bends toward the normal line if the light slows down in the new medium, and it bends away from the normal if it speeds up in the new medium. But how is the angle of refraction related to the angle of incidence? In this experiment you will attempt to answer this question by measuring the angles of incidence and refraction for light passing from air into water and into other transparent materials such as glycerine, oil, alcohol, and glass. You will use the ray-tracing method that you learned when locating images in plane mirrors.

Scientists often prefer to summarize the results of experiments in the form of a graph, rather than just present the results as a large table of numbers. A graph often helps a person to visualize the relationships among the data. If you use your data from this experiment to construct a graph of angle of incidence vs. angle of refraction for water, you could later use the graph to easily predict the angle of refraction for other situations by interpolation.

## semi-circular plastic box 3 pins cardboard water oil glass semicircle straightedge protractor Procedure:

1. With a straightedge, draw a line across the middle of a sheet of paper. Label this line "surface". Label one side of the line "water" (if you are going to use water...) and the other side "air". Place the paper on the cardboard.
2. Fill the semi-circular box with water. (You may use a glass semicircle instead, or some other liquid.) Dry the outside of the box and place it on the paper so that its flat side is on the "surface" line and the curved side lies on the "water" side of the paper.
3. Stick one pin vertically into the paper on the "surface" line at the middle of the flat side of the box. If the box has a clear vertical line marked at this position, the pin may not be needed. This location is where the light ray enters the box. During the experiment, it is important that you do not move the box or this pin!
4. Stick a second pin into your paper a few centimeters from the first pin, but still on the side of the paper towards the flat side of the box. Label this pin "I1" (incidence #1). These 2 pins determine the path of a light ray that enters the flat side of the box.
5. Now, move to the curved side of the plastic box. Looking through the liquid in the box, align your eye so that you see the two pins on the other side of the box in line with each other. Place the last pin several centimeters from the curved side of the box, so that it appears to line up with the other 2 pins as you look through the liquid. Label this pin "R1" (refraction #1). Since the light will only refract at the flat side of the box (Why?), the three pins you have placed trace a light ray from the air through the water.
6. Go back to step 4 and move your "incidence" pin to a new location on the flat side of the box to produce a new angle of incidence. Do not move the pin on the "surface" line. Then repeat step 5 to locate the "refraction" pin for this angle. Label these pins "I2" and "R2" respectively. Continue in this manner until you have gathered data over as wide a range of angles as possible. You want to have both small, large, and intermediate angles represented in your data. Try to have at least 15 data points for each substance.
7. When you have finished taking data for water (or whatever substance you used for the first set of trials), get some other transparent liquid or a solid glass semicircle. Repeat steps 1-6 for this substance.

## Results:

1. Create a data table for each substance that you examined in your experiment. Although there is an angle of incidence and an angle of refraction, it is usually more convenient to talk about the "angle in air" or the "angle in water" instead. Make 3 columns and label them "Trial", "Angle in air, qair (o)", and "Angle in water, qwater (o)". Here, the "q" is the Greek letter "theta", which is commonly used to represent angles. Hopefully I don't have to mention that if you are using glass instead of water, you label the columns qglass, or whatever...
2. On your data sheet, carefully draw and label a normal (perpendicular) to the surface through the center pin location.
3. Carefully draw and measure each angle in air and angle in the other substance and place the numbers in the data table.
4. Construct a graph of "Angle in Air" vs. "Angle in Water" (or whatever) for each substance. Put the angle in air on the horizontal axis. Use an entire sheet of graph paper for each graph, and make the graph as large as is reasonable convenient. You may be able to plot the graph of both substances on the same graph, but if you do use different colors (or something) to indicate which substance each point belongs to. Be sure to label the axes and title the graph - don't forget to indicate which substance is which on the graph.
5. Draw the BEST SMOOTH CURVE through the data points. (This curve may not be a straight line...)

## Conclusions:

Write a short paragraph summarizing your results in this experiment.

## References:

Haber-Schaim, et. al., PSSC Laboratory Guide, 4th Edition, p. 5

Genzer, Laboratory Investigations in Physics, p. 167

last update November 24, 1998 by JL Stanbrough