The critical angle and the refractive index of a media are related by the formula:
sinθc=(μ1)...(1)
Substitute the value of the critical angle into equation (1) and solve to calculate the refractive index of the medium.
sin45∘=⇒⇒μ121=μ1μ=2
The refractive index of the medium can also be written as
μ=vc...(2)
Substitute the values of the known parameters into equation (2) and solve to calculate the required speed of light within the medium.
2=⇒=v3×108ms−1v=23×108ms−12.12×108ms−1