A ray of light is refracted from medium 1 to medium 2. Show that the ratio of the sine of the angle of incidence and the sine of the angle of refraction is equal to the ratio of speed of light in medium 1 and that in medium 2.

Explanation

if the absolute refractive indices of medium 1 and medium 2 are `mu_(1) and mu_(2)` respectively we know,
`(sini)/(sinr) = 1^(mu)2 = (mu^(2))/(mu_(1))`
Now, `" " mu_(1) = ( c )/(v_(1)) [c = "speed of light in vacuum," v_(1) = "speed of light in medium 1"]`
`mu_(2) = (c)/(v_(2)) [v_(2) = "speed of light in medium" 2]`
`therefore " " (mu_(2))/(mu_(1)) = ((c)/(v_(2)))/((c)/(v_(1))) = (v_(1))/(v_(2))`
From (1) and (2) we get,
`(sini)/(sinr) = (v_(1))/(v_(2))`