Physics - Geometrical Optics Question with Solution | TestHub

Let r be the radius of the circle through which other objects become visible. The ray of light must be incident at critical angle C.

$\sin C=\frac{1}{\mu }=\frac{r}{\sqrt{r^2+h^2}}$

${\mu }^2{r}^2=r^2+h^2\Rightarrow \left({\mu }^2-1\right)r^2=h^2$

$\Rightarrow r=\frac{h}{\sqrt{{\mu }^2-1}}$

$\therefore \mathrm{ }\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}=2r=\frac{2h}{\sqrt{{\mu }^2-1}}$