A question about light and refraction ?

Question

A beam of light travelling through a vacuum hits a block of glass at an incidence angle of 60 degrees. The beam propagates through the glass, but gets refracted, with an angle of refraction of 30 degrees. what is the ligths speed of propagation in the glass.

Answer 1

Use Snell's law. Suppose v1 and v2 is the original speed of light before refraction and v2 the speed of light in the medium then,

v2 sin(60) = v1 sin(30)

v2 = v1 sin(30)/sin(60)  = 0.577 v1 (to three decimal places)

Since there's not much difference between the speed of light in air and in vacuuo if we replace v1 with c (the speed of light in a vacuum) we get,

v2 = 173085256.33 m/s

Answer 2

Snell's Law shows that sin i/sin r = refractive index

so sin 60/sin30 = 0.886 /0.5 = 1.772

this is the same fraction as the ratio of the velocity of light in a vacuum to velocity in the medium

3 x 10 ^8 /1.772 = 1.69 x 10^8