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

Here, `angleA = 60^(@)` and n = 1.524
For a ray to suffer total internal reflection at the second face of the prism
`angler_(2) = anglei_( c)` where `i_( c)= sin^(-1) (1/n) = sin^(-1) (1/1.524) = sin^(-1) (0.6526) = 41^(@)`
As `angleA = angler_(1) + r_(2)`
Hence, `angler_(1) = angleA - angler_(2) = angleA - anglei_( c) = 60^(@) - 41^(@) = 19^(@)`
As `(sin i)/(sin r_(1)) =n`,
`therefore anglei = sin^(-1) (0.4962) = 29.75^(@) = 30^(@) =n`