# The Joly Photometer: Measuring Light Intensity Using the Inverse Square Law

 Difficulty Time Required Average (6-10 days) Prerequisites None Material Availability Readily available Cost Low (\$20 - \$50) Safety Adult supervision is recommended for cutting wax.

## Abstract

You have probably seen light bulbs with different wattages, for example 50 W or 100 W. Higher-wattage lights are brighter but they also consume more electrical power. Are some bulbs more efficient than others, meaning they produce more light per unit of electrical power? You can find out for yourself by making a simple photometer to compare the light output from different bulbs. This project shows you how.

## Objective

The goal of this project is to measure the relative intensity of different light bulbs, using a simple photometer that you can build yourself.

## Credits

Andrew Olson, PhD, Science Buddies

Sources This science project is based on:

### MLA Style

Science Buddies Staff. "The Joly Photometer: Measuring Light Intensity Using the Inverse Square Law" Science Buddies. Science Buddies, 24 Oct. 2015. Web. 24 June 2017 <https://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p031.shtml>

### APA Style

Science Buddies Staff. (2015, October 24). The Joly Photometer: Measuring Light Intensity Using the Inverse Square Law. Retrieved June 24, 2017 from https://www.sciencebuddies.org/science-fair-projects/project_ideas/Phys_p031.shtml

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Last edit date: 2015-10-24

## Introduction

As you move away from a light source, the light gets dimmer. No doubt you've noticed this with reading lamps, streetlights, and so on. The diagram at right shows what is happening with a picture. At the center, the yellow star represents a point source of light. Imagine the light from the star spreading out into empty space in all directions. Now imagine the light that falls on a square at some arbitrary distance from the star (d = 1, yellow square). Move away, doubling the distance from the star (d = 2). The light from the original square has now "spread out" over an area of 4 (= 22) squares. Thus, at twice the original distance, the intensity of the light passing through a single square will be 1/4 of the original intensity. Going out still further, tripling the original distance (d = 3), and the light from the original square now covers an area of 9 (= 32) squares. Thus, at three times the original distance, the intensity of the light passing through a single square will be 1/9 of the original intensity. This is what is meant by the inverse square law. As you move away from a point light source, the intensity of the light is proportional to 1/d2, the inverse square of the distance. Because the same geometry applies to many other physical phenomena (sound, gravity, electrostatic interactions), the inverse square law has significance for many problems in physics.

In this project you'll build a simple photometer, invented by the Irish scientist, John Joly. As you'll see, the design of the photometer is based on the inverse square law. In the Joly photometer, two equal-sized blocks of paraffin wax are separated by a layer of aluminum foil. The wax blocks are mounted in a box with windows cut out on the left, front, and right sides, as shown in Figure 1.

Figure 1. Diagram of a Joly photometer. Inside the box are two equal-sized blocks of paraffin wax, separated by a sheet of aluminum foil.

The photometer is positioned between two light sources (see Figure 2). The two light sources and the center of the photometer should all be at the same height. Light from the first source illuminates the left-hand paraffin block. Light from the second source illuminates the right-hand paraffin block. To insure uniform illumination, the distance from each light source to the photometer should be relatively large compared to the size of the wax block. Also, there should be no other light sources in the room. The experimenter views the photometer through the front window and moves it back and forth between the two light sources until both blocks appear equally bright. The photometer should be moved along an imaginary straight line connecting the two light sources.

Figure 2. Schematic diagram of Joly photometer experimental setup. See text for details.

When the two wax blocks are equally illuminated, the relationship between the intensities of the two light sources is determined by the inverse square law. Here is the relationship in the form of an equation:

You can build your own Joly photometer and use it to measure the relative intensity of different light bulbs. Using the wattage of each bulb, you can also compare how efficient different bulbs are at producing light.

## Terms and Concepts

To do this science project, you should do research that enables you to understand the following terms and concepts:
• Inverse square law
• Photometer
• Incandescent light bulbs
• Compact fluorescent light bulbs

Questions

• How do incandescent light bulbs work?
• How do incandescent light bulbs wear out?
• How do compact fluorescent light bulbs work?
• How do incandescent light bulbs wear out?
• Which type of bulb lasts longer?
• Which type of bulb is more efficient at producing light?

## Bibliography

For information on the inverse square law, see:
To learn more about John Joly, the inventor of the Joly photometer, check out the article below. Note that you'll need to download the PDF of the document from the menu bar on the right-hand side of the page.

This science project is based on:

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## Materials and Equipment

• Box of paraffin wax (1-lb. box, contains 4 slabs)
• Sharp knife for cutting wax
• Aluminum foil
• Small cardboard box; Note: the box that the paraffin wax comes in will work well.
• Scissors
• Identical light fixtures, such as a clamp-on work lamp (2)
• Measuring tape
• Light bulbs to test (at least 3 different wattages). Make sure the bulbs you test are all the same type, for example, incandescent, compact fluorescent (CFL), or light-emitting diode (LED); and make sure they are all the same color (for example "warm white," "soft white," "cool white," or "daylight"). See the Variations section if you want to test different types of bulbs.
• Lab notebook

## Experimental Procedure

Building the Photometer
1. You should be able to find one-pound boxes of paraffin wax at your local grocery or hardware store. Each box contains four slabs of paraffin wax.
2. Cut one slab of the wax in half with a sharp knife. Work carefully so that you don't chip or break the slab.

3. Cut a piece of aluminum foil to the same size as your two blocks of wax, and place it in between them.

4. Mount the wax blocks inside a small cardboard box, with windows cut on three sides, as shown. If needed, use tape and small pieces of cardboard to stabilize the wax.

Experimental Setup

1. The illustration is a schematic diagram of the experimental setup.

2. Place the photometer in between two light sources.
1. Each wax block is illuminated by only one of the sources. The aluminum foil prevents light from passing between the blocks.
2. The light sources and the photometer should be at the same height.
3. The photometer should be positioned on the straight line between the two sources.
4. The two light sources should be the only sources of light in the room. No bright sunlight!
5. To insure uniformity of illumination at the photometer, the distance from the photometer to the nearest light source should be large compared to the size of the wax block.
3. Move the photometer back and forth between the two light sources until the the two wax blocks are equally bright.

1. When the wax blocks are equally illuminated, the inverse square law says that the intensities of the two light sources are related by the following equation:

2. Choose one light bulb as your standard, for example, a 60 W soft white bulb. Call this light I1. The intensity of the second light is then given by:

3. Measure the distance from each light source to the aluminum foil layer of the Joly photometer.
4. Calculate the relative intensity of each bulb compared to your standard bulb. (Your standard bulb will have an intensity of 1.0. You can check this by using two identical bulbs. It's a good way to show that your photometer works as expected.)
5. To calculate the efficiency of each bulb, divide the relative intensity by the bulb wattage. Are some bulbs more efficient than others?

## Variations

• Compare the output of incandescent vs. CFL vs. LED bulbs. Pay attention to the equivalent and actual wattages of CFL and LED bulbs. For example, an LED bulb might be listed as "9 W, 60 W replacement." This means that it only uses 9 W, and is supposed to replace a 60 W incandescent bulb, so you should compare it to a 60 W incandescent. Also make sure that all the bulbs you test are the same color (for example "warm white").
• Using your measurements, can you figure out how to compare the cost of using each type of bulb in order to provide an equal amount of light? Your cost comparison should include the cost to purchase each bulb, the cost of electricity for each bulb, and the lifetime of each bulb.
• Each bulb should have a brightness rated in lumens on the package. How do the brightnesses in lumens compare to your measurements? Are the ratios between bulbs the same?
• Compare the output of a candle to a light bulb.

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