How do scientists calculate redshift/blueshift in light?

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I understand that redshift/blueshift is defined as the change in wavelength of the light divided by the wavelength of the light if the source was not moving. But if what we receive has already redshifted/blueshifted, how do we know that it is not the original wavelength of the light?

Also, once we find out that the light received by us has redshifted/blueshifted, how do we find the original wavelength of the light?

In: Physics
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I believe they use the known spectrum for energized hydrogen and helium (known spacing). And look for those lines shifted.

We look for patterns we know. Various atoms and molecules absorb and emit light at very specific frequencies. The best know is probably the Balmer series, which are given off by hydrogen ([https://en.wikipedia.org/wiki/Balmer_series](https://en.wikipedia.org/wiki/Balmer_series)).

Since basically everything in the universe contains at least some hydrogen, and definitely all the far away things we can see like stars, we can look for the Balmer series lines and see what frequency we’re seeing compared to we know what they must have been when they were emitted. That tells us how far they red- or blue-shifted.

You might want to ask “how do you know a line didn’t shift on top of some other line?”. Good question…since the series is multiple lines, we can look for the correct spacing. Even if one line moves over to where we’d expect another one, the whole series will shift the same way so we can look for the unique pattern.

Edit: there is a tacit assumption here that atoms elsewhere in the universe work like the ones we can actually directly test. We have zero evidence that that’s *not* true (and if it’s not, then a bunch of other cosmology is suspect) but it’s technically possible.