The refracting angle of a glass prism is `60^@` and `mu` of its material is `1.45`. Calculate angle of incidence at the first that will just reflect internaly the ray at the second face.

Answer

`24.2^@`

Explanation

Here, `A = 60^@, mu = 1.45, i_1 = ?`
From `mu = (1)/(sin C)`,
`sin C = (1)/(mu) = (1)/(1.45) = 0.6897`
`C = sin^-1 (0.6897) = 43.6^@`
For total internal reflection at `2 nd` face of prism,
`r_2 = C = 43.6^@`
From `r_1 +m r_2 = A`,
`r_1 = A - r_2 = 60^@ - 43.6^@ = 16.4^@`
From `mu = (sin i_1)/(sin r_1)`,
`sin i_1 = mu sin r_1 = 1.45 xx sin 16.4^@`
=`1.45 xx 0.2823 = 0.4093`
`:. i_1 = sin^-1 (0.4093) = 24.2^@`.