Question

A parallel glass slab of refractive index $\sqrt{3}$ is placed in contact with an equilateral prism of refractive index $\sqrt{2}$. A ray is incident on left surface of slab as shown. The slab and prism combination is surrounded by air. Find the magnitude of minimum possible deviation (in degrees) of this ray by slab-prism combination.

Answer 1

The slab does not object for minimum deviation by prism, thus for minimum deviation, we use $r_{1}=r_{2}=30^{\circ}$ as shown in figure

$\Rightarrow \sin i=\sqrt{2} \sin 30^{\circ}$ or $i=45^{\circ}$
Thus minimum deviation $=2 i-A=90^{\circ}-60^{\circ}=30^{\circ}$
$\Rightarrow \sin i=\sqrt{2} \sin 30^{\circ} \text { or } i=45^{\circ}$