Define critical angle with reference to total internal reflection.
Calculate the critical angle for glass-air surface, if a ray of light which is incident in air on the glass surface is deviated through 15°, when angle of incidence is 45°.

Explanation

The critical angle for a pair of media may be defined as the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90° and beyond which the light is totally internally reflected back in the denser medium itself. In present problem angle of incidence in air i = 45°.
As the ray deviates through 15° on entering into glass and glass is optically denser, hence,
`r = 45^(@) 15^(@) = 30^(@)`
`therefore` Refractive index of glass `n_(ga) = (sin i)/(sin r) =(sin 45^(@))/(sin 30^(@)) = (1//sqrt(2))/(1//2) = sqrt(2)`
`therefore` Critical angle for glass-air interface is given by `sin i_( c) = 1/(n_(ga)) = 1/sqrt(2) rArr i_( c) = sin^(-1) (1/sqrt(2)) = 45^(@)`