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 prism is `1.524`.

Explanation

`i_1 = ?,A = 60^@, mu = 1.524`
As `mu = (1)/(sin C)` and from Fig.
`C = r_2` (for total internal reflection at face `AC`)
`:. sin C = sin r_2 = (1)/(mu)=(1)/(1.524) = 0.6561` `:. r_2 = 41^@`
As `r_1 + r_2 = A :. r_1 = A - r_2 = 60^@ - 41^@ = 19^@`
As `mu = (sin i_1)/(sin r_1) :. sin i_1 = mu sin r_1`
`:. sin i_1 =, 1.524 sin 19^@ = 1.524 xx 0.3256 = 0.4962 :. i_1 = sin^-1 (0.4962) = 29^@ 45'`.