<p>The non-relativistic formula can be derived analogously to the derivation of the <a href="https://en.wikipedia.org/wiki/Doppler_effect" rel="nofollow noreferrer">Doppler effect for sound</a>. Namely, draw waves as consecutive parallel lines moving at velocity <span class="math-container">$c$</span> whose distance is <span class="math-container">$\lambda$</span> (if the source is not moving) and let the source move away at <span class="math-container">$v$</span>. You will find that the distance has increased and became the observed wavelength, which is <span class="math-container">$\lambda$</span> - <span class="math-container">$vt$</span> = <span class="math-container">$\lambda + v\lambda/c$</span> = <span class="math-container">$\lambda(1+\frac{v}{c})$</span>.
<br>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.</p>

CC BY-SA 4.0
2020-02-29T09:58:11.413Z
To OP. Beware that in cosmology there is a third kind of "Doppler“ shift. That one due to expansion. My comment might be unrelated or unrccessary, though.
Alchimista
CC BY-SA 4.0
2020-03-02T09:45:12.537Z
fyi I've just asked [Is there still a red shift when moving perpendicular to the direction of incidence?](https://astronomy.stackexchange.com/q/35382/7982) It isn't necessarily relevant here but I'm just mentioning it for completeness.
uhoh
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2020-02-28T21:48:44.783Z
2020-02-29T19:53:50.757Z
2020-02-29T19:53:50.757Z
Tosic
<p>I was wondering where does the formula for redshift <span class="math-container">$$z=\frac vc$$</span> come from? Can it be derived from the definition of redshift <span class="math-container">$$z={\lambda_{observed} - \lambda_{emitted}\over \lambda_{emitted}}?$$</span> </p>

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2020-03-01T01:18:10.993Z
Cool! I've just asked [How to best format the question mark that immediately follows an equation in a question sentence?](https://math.meta.stackexchange.com/q/31283/284619)
uhoh
<redshift>
Redshift Formulas
space nerd
# Redshift Formulas

(Asked by: username_0 on 2020-02-28)

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

**Tags:** redshift
> **Comments:**
> **username_1**: Cool! I've just asked [How to best format the question mark that immediately follows an equation in a question sentence?](https://math.meta.stackexchange.com/q/31283/284619)  

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## 1 answers

### Answer by username_2 on 2020-02-28. Score: 3 | Accepted answer

The non-relativistic formula can be derived analogously to the derivation of the [Doppler effect for sound](https://en.wikipedia.org/wiki/Doppler_effect). 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.

> **Comments:**
> **username_3**: To OP. Beware that in cosmology there is a third kind of "Doppler“ shift. That one due to expansion. My comment might be unrelated or unrccessary, though.  
> **username_1**: fyi I've just asked [Is there still a red shift when moving perpendicular to the direction of incidence?](https://astronomy.stackexchange.com/q/35382/7982) It isn't necessarily relevant here but I'm just mentioning it for completeness.  

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