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)/(sin r_(1)) :. sin i_(1) = mu sin r_(1)`
`:. sin i_(1) = 1.524 si n 19^(@) = 1.524 xx 0.3256 = 0.4962 :. i_(1) = sin^(-1) (0.4962) = 29^(@)45'`