Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$ , a ray , incident at an angle $\theta$ , on the face AB would get transmitted through the face AC of the prism provided :

Question

$\begin{array}{1 1} \theta > \sin^{-1} \bigg[ \mu \sin \bigg(A - \sin ^{-1}\bigg(\frac{1}{\mu}\bigg)\bigg) \bigg] \\ \theta > \cos^{-1} \bigg[ \mu \sin \bigg(A + \sin ^{-1}\bigg(\frac{1}{\mu}\bigg)\bigg) \bigg] \\ \theta < \cos^{-1} \bigg[ \mu \sin \bigg(A + \sin ^{-1}\bigg(\frac{1}{\mu}\bigg)\bigg) \bigg] \\ \theta > \sin^{-1} \bigg[ \mu \sin \bigg(A - \sin ^{-1}\bigg(\frac{1}{\mu}\bigg)\bigg) \bigg] \end{array} $