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

sin `i_(e) = (1)/(n) = (1)/(1.524) = 0.6562 " " therefore i_(e) = 41^(@)`
i.e., `r_(2) = i_(e) = 41^(@)`
`r_(1) + r_(2) = A `
`r_(1) = A - r_(2) = 60 - 41 = 19^(@)`
`(sin i_(1))/(sin r_(1)) = n " " therefore sin i_(1) = n sin r_(1) = 1.524 sin 19^(@) = 0.4962 `
`i_(1) = sin^(1) (0.4962) i_(1) = 29^(@) 45. approx 30^(@)` .