A ray of light incident on the horizontal surface of a glass slab at `70^@` just grazes the adjacent vertical surface after refraction. Complete the critical angle and refractive index of glass.

Explanation

Let AB is incident ray and BC is refracted ray through glass slab.
Then `r + C + 90^(@) = 180^(@)`
r + C = 90
r = 90 - C
From `mu = (1)/(sin C) = (1)/(sin (90^(@)-r)) = (1)/(cos r)`
From `sin r sqrt(1- cos^(2)r) = sqrt(1-((1)/(mu))^(2)) = sqrt(mu^(2)-1)/(mu)`
By Snell's law `mu = (sin i)/(sin r)`
`sin i = mu sin r = (musqrt(mu^(2)-1))/(mu)`
`sin i = sqrt(mu^(2) - 1)` or `mu = sqrt(1+ sin^(2)70^(@))`
`mu = sqrt(1+(0.9397)^(2)) = 1.372`
`sin C = (1)/(mu) = 0.7289`
`C = 46^(@)47'`