Redshift Formulas

I was wondering where does the formula for redshift $$z=\frac vc$$ come from? Can it be derived from the definition of redshift $$z={\lambda_{observed} - \lambda_{emitted}\over \lambda_{emitted}}?$$

• – uhoh Mar 1 at 1:18

1 Answer

The non-relativistic formula can be derived analogously to the derivation of the Doppler effect for sound. Namely, draw waves as consecutive parallel lines moving at velocity $$c$$ whose distance is $$\lambda$$ (if the source is not moving) and let the source move away at $$v$$. You will find that the distance has increased and became the observed wavelength, which is $$\lambda$$ - $$vt$$ = $$\lambda + v\lambda/c$$ = $$\lambda(1+\frac{v}{c})$$.
Note that this formula is not relativistic and that there is cosmological (as pointed out by @Alchimista in the comment below) as well as gravitational redshift, so the formula above only describes only one of the effects that cause redshift or blueshift.