# Snell's Law Lab

 Materials: Computer and School Network Protractor Time Allotment: 4 Class Days

### Purpose:

The purpose of this lab is to investigate the refraction of light as it passes from air into, through, and out of a hemi-cylindrical (half-circle cylinder) disk made of an unknown material. Measurements of the angle of incidence and the angle of refraction will be measured and the index of refraction of the unknown material will be determined.

### Pre-Lab Analysis:

1. A hemi-cylindrical disk made of an unknown material is placed on the tabletop. A top view of the block is shown at the right. A laser beam is directed towards the flat side of the disk, refracts as it passes into the material and continues through the material as shown. On the diagram, draw a normal at the entry point of the laser beam and label the angle of incidence and angle of refraction at this point.
2. Measure and record the angle of incidence and the angle of refraction for the laser beam entering the glass semi-circle.

 Angle of I = _______ deg Angle of R = _______ deg

3. Substitute values of the angle of incidence and the angle of refraction into Snell's law in order to determine the index of refraction of the unknown material. Show all your work in the space below.

4. Explain why the laser light does not refract upon exiting across the curved side of the half-circle.

In this lab, the index of refraction of the unknown material will be determined using a graphical method. Since any given measurement/calculation may be in error, we will make several measurements for a range of values from 0 degrees and 80 degress. (By using a range of values, the errors resulting from mismeasurement will be averaged out.) The corresponding angles of refraction will be measured, and a plot of the sine of the incident angle (I) vs. the sine of the refracted angle (R) will be constructed. The plot should be linear, having the equation of

sine (I) = slope * sine (R) + y-intercept

This equation bears strong resemblance to a rearranged version of the Snell's law equation for light passing from air into the unknown material.

nair * sine (I) = nunknown * sine (R)

For the equation representing the experimental data and the theoretical equation (Snell's law) to be equivalent, the slope of the line would have to be equal to the index of refraction of the unknown material and the y-intercept of the line would have to be 0.

### Procedure:

To begin this lab:

1. Log on to the student server in the usual manner
2. Open the Multimedia folder; then open the Hypercard application.
3. Once the Hypercard is opened, chose Open... from the File menu.
4. A directory dialogue box should appear. Navigate through the Physics Stacks directory and find the file titled Snell's Law; open this stack by double-clicking on its icon.
5. Click anywhere on the first card in order to navigate to the simulation card.

Collecting the Data:

In this lab, you will use the line of sight method in order to determine the path of light through a solid half-circle of an unkown material. The unknown material has a an etch mark on its flat side. An object pin will be placed a given distance from the flat side. You will look through the curved side and adjust your line of sight until your line of sight is aligned with the path of the light ray from the pin to the etch mark through the material and to your eye. When you have properly adjusted your line of sight, it will appear as though your eye position, the etch mark and the image of the object pin are aligned. At this position, a light ray traveling from the object pin to the etch mark will refract upon entering the unkown material and travel straight to your eye. Since the path of the light ray is known, the angles of incidence and refraction can be measured and the index of refraction can be calculated.

1. The object pin on the flat side of the half-circle is shown. Click on the lower-left side of the half-circle at the location where you believe that a light ray from object to etch mark will exit the half-circle. Once you click on the card, the screen will be updated and a side view of the object pin and etch mark will be shown (see above discussion).
2. Use the side view (see above discussion) and a trial-and-error method to find the precise location of the eye in order to view the light ray which passes from the object pin through the etch mark and out of the half-circle. Once you have found an appropriate location of the eye, record the angle of refraction in the data table below.
3. The computer will prompt you to either enter a new angle of incidence or to allow it to randomly select a new angle of incidence. Take either choice and repeat steps 1 and 2 until you have collected a set of 10 data pairs for the angle of incidence and the corresponding angles of refraction. For accurate results, be sure to use angles of incidence ranging between 0 degrees and 80 degrees.

4. Once you have completed Table I, repeat steps 1-3 for a different material. To change the material which the half-circle disk is made of, click on the "Try New Index of Refraction" button. Once more, collect at least 10 data pairs for the second material and record in Table II.

5. Using a calculator, determine the sine of the angle of incidence and the angles of refraction. Use Snell's law to calculate the index of refraction of the unknown material as would be predicted from each pair of measurements.

Graphical Representation and Analysis of the Data:

Now that you have collected the data for two different materials, you will analyze the data in order to draw some generalizations. Using the Graphical Analysis program (available on the school servers), plot values of the sine (I) vs. sine (R); the sine (I) values shuld be plotted along the y-axis. Click on the graph and check the Graph menu to be sure that Statistics, Regression Line, and Point Protectors are activated. Print a graph of each data set and include with your final lab report. Each graph should be labeled to indicate which data set (I or II) is being plotted. Once you have completed the graphs, answer the questions in the Analysis of the Data section.

### Data:

Table I - Investigation of the First Unknown Material

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(degrees)

### Index of Refraction

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Table II - Investigation of the Second Unknown Material

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### Analysis of the Data:

1. Analyze data tables for the two data sets. What do you notice about the loast column of data (the index of refraction)? Discuss.

2. Write an equation for the line on each graph. (If necessary, refer to the discussion above.)

 Data Set I Data Set II ____________________ ____________________

3. What physical quantity does the slope of the line represent? Explain your answer. (If necessary, refer to the discussion above.)

4. Identify the index of refraction for each material.

 Data Set I Data Set II ____________________ ____________________

Explain how you found your answers.

5. Comment on the accuracy of your data. What is it about the graph and the data tables which indicate to you that your data set is either accurate or inaccurate? Explain.

### Post-Lab Questions:

1. Use Snell's Law to determine the path of the light through this glass (n=1.5) parallelogram. Draw a normal, perform the appropriate measurements and calculations for the entry point and draw the refracted ray for the light entering the glass. Continue the ray to the opposite side, draw a normal, perform the appropriate measurements and calculations for the exit point and draw the refracted ray for the light exiting the glass. Show your calculations in the space below.

2. Use Snell's Law to determine the path of the light through this glass (n=1.5) triangle. Draw a normal, perform the appropriate measurements and calculations for the entry point and draw the refracted ray for the light entering the glass. Continue the ray to the opposite side, draw a normal, perform the appropriate measurements and calculations for the exit point and draw the refracted ray for the light exiting the glass. Show your calculations in the space below.

### Conclusion:

Summarize what you have learned about the refraction of light through a hemi-cylindrical disk. Do a bang-up job!

This page created by Tom Henderson and last updated on 8/22/97.