Question

A ray is incident on a sphere of refractive index $\sqrt{2}$ as shown in figure. Angle of refraction of the ray inside sphere is ${30}^{\circ }$ and ray underdoes TIR as shown. If total deviation suffered by the ray is $x\times {30}^{\circ }$, then find $x$.

Answer 1

Using Snells Law,
$\frac{\sin i}{\sin r}=\sqrt{2}\Rightarrow i={45}^{\circ }$
$\text{Total deviation}$
$=({45}^{\circ }-{30}^{\circ })+{180}^{\circ }-2\left({30}^{\circ }\right)+({45}^{\circ }-{30}^{\circ })$
$={30}^{\circ }+{120}^{\circ }$
$={150}^{\circ }=30x$
$x=5$