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

n= 1.5
Refractive index `n= (1)/(sin C)`
`C= sin^(-1) ((1)/(n))= sin^(-1) (0.666) = 42^(@)`
We know that `A= r_(1) + C`
`r_(1)= A + C = 60^(@)- 42^(@) = 18^(@)`
`n= (sin i)/(sin r_(1))`
`1.5 = (sin i)/(sin 18^(@))`
`sin i= 0.4635`
`i= 28^(@)`