A monochromatic light is incident from air on a refracting surface...

For T.I.R at coating
$sinc = \dfrac{n}{\sqrt{3}}$ …(i) \left[sin C = \dfrac{{n}_{2}}{{n}_{1}}\right]$<br/>Appling Snell's law at first surface<br/>$sin \theta = \sqrt{3}\sin \left(75 - c\right)$<br/>for limiting conduction, at$\theta = {60}^{o}$<br/>$\sin 60 = \sqrt{3}\sin \left(75 - c\right)$<br/>$\dfrac{\sqrt{3}}{2} = \sqrt{3}\sin \left(75 - c\right)$<br/>$\begin{cases}\dfrac{1}{2} = \sin \left(75 - c\right) & ⇒ & \sin 30 = \sin \left(75 - c\right) \\ ⇒ 30 = 75 - c & ⇒ & c = {45}^{o} \\ Using\left(i\right)\dfrac{n}{\sqrt{3}} = \dfrac{1}{\sqrt{2}} & ⇒ & {n}^{2} = \dfrac{3}{2} = 1.50\end{cases}