A rectangular block is composed of three different glass prisms (… - Vidyadip

MCQ

A rectangular block is composed of three different glass prisms (with refractive indices $\mu_1, \mu_2$ and $\mu_3$ ) as shown in the figure below. A ray of light incident normal to the lef $t$ face emerges normal to the right face. Then, the refractive indices are related by

A
$\mu_1^2+\mu_2^2=2 \mu_3^2$
B
$\mu_1^2+\mu_2^2=\mu_3^2$
✓
$\mu_1^2+\mu_3^2=2 \mu_2^2$
D
$\mu_2^2+\mu_3^2=2 \mu_1^2$

✓

Answer

Correct option: C.

$\mu_1^2+\mu_3^2=2 \mu_2^2$

c
(c)

Ray diagram of ray through the composition of prisms will be

By Snell's law on surface $A B$ and $A C$, we have

$\mu_1 \sin 45^{\circ}=\mu_2 \sin \theta \quad \dots(i)$

and $\mu_3 \sin 45^{\circ}=\mu_2 \cos \theta \quad \dots(ii)$

As $\alpha-\theta=45^{\circ}$, from figure

Squaring and adding Eqs $(i)$ and $(ii)$, we get $\quad \frac{\mu_1^2}{2}+\frac{\mu_3^2}{2}=\mu_2^2$

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