The inverse square law for intensity |
Thus, if you double the distance to a light source the observed intensity is decreased to (1/2)^{2} = 1/4 of its original value. Generally, the ratio of intensities at distances d_{1} and d_{2} are
Thus, if you have a known distance to a star and are able to measure the flux at that distance, the total energy output of the star can easily be ascertained (this will be shown in class).
A simple way to think about this, is the following:
This means the total energy output is your measured flux multiplied by the surface area:
So, at R = 1 meter f = 4 million photons per square cm per second ; the total surface area is 4p square meters (or 40,000 square centimeters) so the total Energy emitted is 40,000 x 4 million photons per second.
Now notice, at R = 2 meters f is down to 1 million photons per square cm per second but the total surface are has increased to 16p square meters or 160,000 square centimeters. So the total Energy is 160,000 x 1 million photons per second, which is the same number as before.
Thus if you can measure f at a known distance, then you know the intinsic energy output. The ability to measure f, however, depends upon the DETECTOR!
Example of Inverse Square Law Applet (Point Mode)
Area Mode (right click in the box!)
First Set of Exercises:
Second Set of Exercises:
Third Set of Excercises: