# Using the Law of Reflection to Measure Heights

## Equipment: small bowl meter stick water small mirror dark colored paper measuring tape Discussion:

It is very easy to use the Law of Reflection and some simple geometry to measure the height of an object that would be very difficult to measure directly. Please study the diagram below.

In this diagram, a person observes the image of the top of a flagpole, using the surface of a bowl of water as the reflecting surface. The Law of Reflection guarantees that the two triangles formed are similar (Do you see why?)

In the diagram below, "h" is the height of the person's eyes above the surface of the water, and "d" is the horizontal distance from the person to the center of the bowl. "H" represents the height of the flagpole, and "D" is the horizontal distance from the flagpole to the bowl of water. The 3 distances h, d, and D are easy to measure.

## Notes & Suggestions:

Your instructor will pick a tall object for you to measure. When you finish your calculations, you can compare your value for the height with the value obtained by the other lab groups in the class.

If you have trouble seeing the image of the object in the surface of the water:

• Try putting some dark-colored paper in the bottom of the bowl.
• If a breeze disturbs the surface of the water, making it difficult to see the image, you can try floating a small mirror on the surface of the water.

You should make two sets of measurements - one with a meter stick and one with a long measuring tape. You need to decide:

• How will you determine the precision (or uncertainty) of your measurements?
• What is the major source of uncertainty in your measurements?
• What is the precision in your measurements?

If you are so inclined, a spreadsheet program can be used to perform your calculations:

In your lab book, be sure to:

• Describe the procedures you used.
• Include your original data table.
• Show a sample calculation.
• Clearly state your results - what is your best estimate for the unknown height and your estimated uncertainty.
• In your conclusions:
• What are the major sources of uncertainty in your lab? If you had more time, what would you do to improve the precision of your results?
• How do your results compare to the results of the other groups? If there are major discrepancies in the results, why do you think this occurred? Taking all of the results of the class into consideration, how would you modify your results?

## References:

adapted from IHETS AP Physics Lab #2 - September 1992

last update August 14, 1997 by JL Stanbrough