The Doppler Effect of Light equation is used to evaluate how fast a source and observer are moving either towards, or away from each other. It is calculated using:
Note: `beta` is a common substitution for the fraction, `v/c` where `v` is the same as stated above and `c` is the speed of light.
Note: If the object is coming closer to you then you will have to mentally swap the positive and negative signs, if the object is getting further away from you then you can leave it as is.
The doppler effect equation usually relies on the motion of the receiver, the observer and the medium. But when looking at the doppler effect of light, we recognize that light does not have a medium. So we can only rely on the relative motion of our source and observer.
And that motion would be `v`. As stated earlier: `v` is the rate at which the separation between the source and the receiver is increasing. `v` is positive if the separation between the source and receiver is increasing, and it is negative if the separation between the two is decreasing.
The Doppler Effect of Light equation is derived from looking at a different version of the Doppler Effect equation and adding some "relativity" to it.
If we take a look at this equation:
`f = f_0 sqrt((1-(v/c))/(1+(v/c)))`
then divide `f_0` to the left side,
`f/f_0 = sqrt((1-(v/c))/(1+(v/c)))`
if you haven't already noticed, the Doppler Effect of Light equation has `D(v)` on the left side. Which is precisely what `f/f_0` is. `D(v)` is a ratio of the observed and source frequencies!
24.7 Doppler shifts and clock time by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.