Question

Explain the Doppler Effect with regard to its effect on light frequencies. How does this relate to the cosmological redshift?

Answer 1

The Doppler effect:- The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding.

The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc.

Relativistic Doppler Effect for Light:-

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.

The listener receives a frequency f_L which would be different from the frequency transmitted by the source f_S. This is calculated with relativistic mechanics, by applying necessary the length contraction, and obtains the relationship:

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 visible light spectrum, 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."