# Using the Law of Reflection to Measure Heights

## Purpose:

To measure the height of a tall object (tree, light pole, flag pole) using the Law of Reflection.

## 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 ab 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.

## Equipment: small bowl meter stick water small mirror dark colored paper Procedure:

1. Pick a tall object (perhaps your teacher has a suggestion), a flag pole or utility pole, for instance.
2. Put some water in a small bowl, and place the bowl on the ground a few meters from the tall object.
3. Move around until you can see the image of the top of the pole reflected in the water's surface. If you have trouble seeing the reflected image, it may help to put some dark colored paper in the bottom of the bowl. (If a breeze is blowing the water's surface too much to form a clear image, you can carefully float a small mirror on the surface of the water and use the mirror for your reflecting surface.)
4. Measure the distance from the bowl to your feet (d) , the distance from the bowl to the base of the light pole (D), and record them in your data table (A sample data table is shown below).
5. Measure the vertical distance from the bowl to your eye (h).
6. Move the bowl to another distance from the pole, and repeat your measurements until you are satisfied that you have enough data.

## Results:

1. Use similar triangles (as shown above) to calculate the height of your tall object for each trial. Show a sample calculation, and record your results in your data table.
2. Calculate the average height of your measurements.

## Conclusions:

How closely do your height measurements agree? Do you think that this is an accurate way to measure heights? Why? What factors most affect the accuracy of this method?

What is the advantage of using water as a reflecting surface for this activity, instead of just laying a mirror on the ground?

## reference:

IHETS AP Physics Lab #2 - September 1992

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last update August 14, 1997 by JL Stanbrough