The Inverse Square Law of Light

The major thing to next understand, is the relationship between apparent brightness (the energy received by some detector) and the distance to the star.

The intensity of light observed from a source of constant intrinsic luminosity falls off as the square of the distance from the object. This is known as the inverse square law for light intensity.

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 d1 and d2 are

Because of this fall of in light intensity with distance, the intrinsic energy output of stars (also called their luminosity ) can only be known if their distances are known . Later on this term we will be measuring distances to nearby stars using the Parallax applet.

Thus, if you have a known distance to a star and are able to measure the flux from that star (e.g. its apparent brightness), the total energy output of the star can easily be ascertained.

Astronomers call the total energy output of a star its Luminosity .

We will use a simple 100 watt lightbulb and a digital thermometer in class today to demonstrate the principle that, as you move farther away from an isotropic light source (e.g. the lightbulb), the energy received by that detector, decreases as the square of the distance.

The basic idea is shown in the diagram below. At a distance of 10 feet, the same "cone of light" that goes through 1 square at 5 feet, now goes through 4 squares at 10 feet.

The flux per square at 10 feet is therefore 1/4 that at 5 feet. Flux per square is what we measure as apparent stellar brightness.

Remember, the basic scaling relation is this:

Flux goes as 1/D2

Where D is the distance to the light source.

Thus, if you move a standard lightbulb twice as far away, the energy that you receive goes down by 22; that is you receive 1/4 as less energy. It is this simple reason why distant stars appear faint.

Strange as this may sound, most elementary astronomy students never understand this concept and how to apply it. The second homework assignment will give you this opportunity to apply it.

To serve as a guide, you can play with the following Simulator