At what angle should a ray of light be incident on the face of a prism of refracting angle `60^(@)` so that it just suffers total internal reflection at the other face ? The refractive index of the material of the prism is 1.524.`

Explanation

If the refracted ray in the prism is incident on the second face at the critical angle i c , the angle of refraction r at the first face is `(60^(@)-i_(c))`.
Now, `i_(c) = sin^(-1) (1//1.524) ~= 41^(@)`
Therefore, `r = 19^(@) sin i = 0.4962, i ~= 30^(@)`