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I'll assume that this is the critical angle from the median to a vaccum.

You use Snell's law, n1sin(x1) = n2sin(x2)

where n1 = index of refraction of your median, n2 = 1 (the index of refraction in a vaccum), x1 = the critical angle (45 degrees), x2 = 90 degrees since light comes out at 90 degrees when it is shone on the critical angle.

So...

n1sin(45 degrees) = 1 (sin 90 = 1)

n1 = 1/sin(45 degrees)

n1 = 1.414...

Now the index of refraction is the speed of light in a vaccum over the speed of light in the median so:

1.414... = (3.00 x 10^8 m/s) / v

v = (3.00 x 10^8 m/s) / 1.414...

v= 2.1 x 10^8 m/s

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