Two transparent media A and B are separated by a plane boundary. The speed of light in those media are 1 . 5 × 10 8   m   s - 1 and 2 . 0 × 10 8   m   s - 1 , respectively. The critical angle for a ray of light for these two media is:

Step-by-step solution

Refractive index μ in terms of speed of light c in vacuum and wave speed v in medium is given by, μ = c v . So, for medium A , μ A = c v A = 3 × 10 8 1 . 5 × 10 8 = 2 and for medium B , μ B = c v B = 3 × 10 8 2 × 10 8 = 1 . 5 For critical angle, angle of refraction r = 90 ° . Using Snell's law, μ 1 sin i = μ 2 sin r ⇒ 2 sin i = 1 . 5 sin 90 ° ⇒ sin i = 1 . 5 2 = 0 . 750 ⇒ i = sin - 1 0 . 750