As the distance from a light source increases, the apparent brightness of the source decreases. In this experiment, you will investigate this relationship.
Go to the Direct Measurement Video showing a Joly Photometer. Notice there is a menu where you can select different videos. The video loaded in the browser should be the first video in the list, Intro 1: The Joly Photometer. Click the Play button and watch the video. It demonstrates how to construct and use a Joly Photometer.
Select the video Intro 2: Brightness vs. Distance. Click the Play button and watch the video. It demonstrates how to use a Joly Photometer to compare a source of unknown luminosity with a 10-LED source whose luminosity can be changed by turning off LEDs. The 10-LED source is a way of varying brightness at the wax in a controlled way.
Select the video 9 bulbs. Click the tool Horizontal Ruler Calibrated in order to show a ruler. By clicking and dragging on the ruler, place the 0 mark at the filament of the bulb on the left (guesstimate the location of the filament). Now, using the video control buttons and slider, find the video frame when the apparent brightness of the wax facing the left bulb is the same as the apparent brightness of the wax facing the right bulb.
At this instant, the apparent brightness of the left bulb is the same as the apparent brightness of the right bulb. But the left bulb is farther from the wax than the right bulb. So which bulb (the right bulb or left bulb) has a greater luminosity?
Since the two bulbs have the same apparent brightness (at the location of the wax) and since the distance from the right bulb to the wax remains the same, we can use the number of LEDs as a measure of brightness. Download and open this spreadsheet to record and graph your data. Record the number of LEDs as a unit of brightness, and record the distance from the left bulb.
Use the menu to change the video to 8 bulbs (i.e. 8 LEDs). Again find the location where the brightness of the left bulb and brightness of the right bulb are the same. In your spreadsheet, record the distance from the left bulb and the number of LEDs.
Repeat your measurements for all numbers of LEDs from 9 to 1. Record all data in Excel. You should see a graph of brightness as a function of distance from the left bulb. The trendline shows that brightness is proportional to 1 over distance squared.
Right-click on a data point and select "Add Trendline..." Select the type "Power." Click Options and select "Display equation on chart." You will notice an equation for the best curve-fit (using a power relationship). It has the form y=AxB where A and B are numbers. B should be close to -2, meaning that the equation is y=A/x2. Record the constants A and B in your curve fit.