Light waves from a moving source experience the Doppler effect to result in either a red shift or blue shift in the light's frequency. This is in a fashion similar (though not identical) to other sorts of waves, such as sound waves. The major difference is that light waves do not require a medium for travel, so the classical application of the doppler effect doesn't apply precisely to this situation.
Consider two objects: the light source and the "listener" (or observer). Since light waves traveling in empty space have no medium, we analyze the Doppler effect for light in terms of the motion of the source relative to the listener.

We set up our coordinate system so that the positive direction is from the listener toward the source. So if the source is moving away from the listener, its velocity v is positive, but if it is moving toward the listener, then the v is negative. The listener, in this case, is always considered to be at rest (so v is really the total relative velocity between them). The speed of light c is always considered positive.

f_L = sqrt [(c - v)/(c + v)] * f_S

Red Shift & Blue Shift

A light source moving away from the listener (v is positive) would provide an f_L that is less than f_S. In the , this causes a shift toward the red end of the light spectrum, so it is called a red shift. When the light source is moving toward the listener (v is negative), then f_L is greater than f_S. In the visible light spectrum, this causes a shift toward the high-frequency end of the light spectrum. For some reason, violet got the short end of the stick and such frequency shift is actually called a blue shift. Obviously, in the area of the electromagnetic spectrum outside of the visible light spectrum, these shifts might not actually be toward red and blue. If you're in the infrared, for example, you're ironically shifting away from red when you experience a "red shift."

Applications

Police use this property in the radar boxes they use to track speed. Radio waves are transmitted out, collide with a vehicle, and bounce back. The speed of the vehicle (which acts as the source of the reflected wave) determines the change in frequency, which can be detected with the box. (Similar applications can be used to measure wind velocities in the atmosphere, which is the "Doppler radar" of which meteorologists are so fond.) Even more significantly, evidence from the analysis of light from distant galaxies shows that the light experiences a red shift. These galaxies are moving away from the Earth. In fact, the results of this are a bit beyond the mere Doppler effect. This is actually a result of spacetime itself expanding, as predicted by genera. Extrapolations of this evidence, along with other findings, support the "big bang" picture of the origin of the universe.
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