Question

If a light ray passes through a rectangular glass slab as shown below, then

Answer 1

Answer:

Option (1) $\sin i=\frac{\sin 75^\circ}{\sqrt{3}}$

Explanation:

As shown in figure

If the refractive index of the glass w.r.t. air is n then

By Snell's law

$n=\frac{\sin75^\circ}{\sin r}$

$\implies n=\frac{\sin75^\circ}{\sin 60^\circ}$

Similarly when the ray entres from the glass to the air

$\frac{1}{n}=\frac{\sin 30^\circ}{\sin i}$

$\implies n=\frac{\sin i}{\sin 30^\circ}$

Thus,

$\frac{\sin75^\circ}{\sin 60^\circ}=\frac{\sin i}{\sin 30^\circ}$

$\implies \sin i=\frac{\sin75^\circ}{\sin 60^\circ}\times\sin 30^\circ$

$\implies\sin i=\frac{\sin 75^\circ}{\sqrt{3}/2}\times\frac{1}{2}$

$\implies \sin i=\frac{\sin 75^\circ}{\sqrt{3}}$

Hope this helps.