Question

A ray of red light enters a liquid from air, as shown in figure . The angle $1$ is ${45}^{\circ }$ and $2$ is ${30}^{\circ }$.
(a) Find the refractive index of liquid.
(b) Show in the diagram the path of the ray after it strikes the mirror and re-enters in air. Mark in the diagram the angles wherever necessary.
(c) Redraw the diagram if plane mirror becomes normal to the refracted ray inside the liquid. State the principle used.

Answer 1

(a) Refracted index of the liquid =

${}_a{\mu }_i=\frac{\sin i}{\sin r}$

${}_a{\mu }_i=\frac{\sin {45}^0}{\sin {30}^0}=\frac{1/\sqrt{2}}{1/2}=\sqrt{2}=1.414$

(b) See figure 1

(c) See figure 2

Here the 'Principle of Reversibility of light' is used.