Physics - Geometrical Optics Question with Solution | TestHub

Refractive index of glass with respect to air =$\mu$
Critical angle =$\theta$
$\therefore \mu =\frac{1}{\mathrm{s}\mathrm{i}\mathrm{n}\theta }$…. (i)
When a ray of light incident from air on the glass with angle of incidence$\theta$. If r the angle of refraction, then by Snell’s law,
$\mu =\frac{\mathrm{s}\mathrm{i}\mathrm{n}\theta }{\mathrm{s}\mathrm{i}\mathrm{n}r}$
$\Rightarrow \mathrm{s}\mathrm{i}\mathrm{n}r=\frac{\mathrm{s}\mathrm{i}\mathrm{n}\theta }{\mu }=\frac{1/\mu }{\mu }$[from Eq. (i)]
$\mathrm{s}\mathrm{i}\mathrm{n}r=\frac{1}{{\mu }^2}$
$r={\mathrm{s}\mathrm{i}\mathrm{n}}^{-1}\left(\frac{1}{{\mu }^2}\right)$