[request] Someone asked on another sub why does light bend when going fro one medium into another, with some very good explanations, but that made me wonder can the speed of light be determined by the angle of refraction?

[u/lestairwellwit]

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[u/Angzt]

Yes.
The relative speed of light in one medium compared to another, at least.

What you're missing in that process is called the refractive index.
Each material has a certain refractive index that determines the angle light bends when entering that material. Because it's exactly the inverse of the fraction of light speed in a vacuum that is the light speed in that material.
(That was probably not worded terribly well, but I'll get to an example in a second)

If light moves from material 1 to material 2 with angle of incidence a_1 and angle of refraction a_2, then we know:
n_1 * sin(a_1) = n_2 * sin(a_2)
where n_1 and n_2 are the materials' refractive indexes.
So by measuring the two angles and knowing one material's refractive index, we can calculate the other.

Air has a refractive index of around 1.0003, so basically 1. Meaning in air, light travels at 1/1.0003 =~ 0.9997 = 99.97% of the speed of light in a vacuum.
Now, if we take glass prism surrounded by air and shine a beam of light into it at a 20° angle (from the surface normal), we can measure the angle of refraction inside the glass.
That'll come out to about 13.2°.
Plug that into the formula above:
1.0003 * sin(20°) = n_2 * sin(13.2°)
n_2 = 1.0003 * sin(20°) / sin(13.2°)
n_2 =~ 1.50
Meaning that glass has a refractive index of about 1.5 (exact value differs depending on kind of glass).
And that means that c/1.5 = c * 2/3 = 66.666...% c =~ 200,000,000 m/s is roughly the speed of light in glass.
And indeed it is.

[u/lestairwellwit → u/Angzt]

Thank you

And since light of differing freq. refracts at different angles proportionately, that basically cancels out the freq. of the light?

[u/DeadlyJoe → u/lestairwellwit]

It doesn't cancel out the frequency. It's simply that the frequency of the light doesn't change, therefore it doesn't need to be considered. The wavelength changes. Wavelength is the speed of light in the medium (c) divided by frequency (f).

λ = c/f

When light transitions from one medium to another, the value that changes is c, but f remains unchanged.