A parallel glass slab of refractive index √3 is placed in contact with an equilateral prism of refractive index √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.

Question

A parallel glass slab of refractive index √3 is placed in contact with an equilateral prism of refractive index √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. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The slab does not object for minimum deviation by prism, thus for minimum deviation, we use

r_{1} = r_{2} = 3 0^{\circ}

as shown in figure

\Rightarrow sin i = 2 sin 3 0^{\circ}

or

i = 4 5^{\circ}

Thus minimum deviation

= 2 i - A = 9 0^{\circ} - 6 0^{\circ} = 3 0^{\circ}

\Rightarrow sin i = 2 sin 3 0^{\circ} or i = 4 5^{\circ}

The slab does not object for minimum deviation by prism, thus for minimum deviation, we use r1​=r2​=30∘ as shown in figure ⇒sini=2​sin30∘ or i=45∘ Thus minimum deviation =2i−A=90∘−60∘=30∘ ⇒sini=2​sin30∘ or i=45∘