1)

A right-angled prism of refractive index  $\mu_{1}$ is placed in a rectangular block of refractive index $\mu_{2}$, which is surrounded by a medium of refractive index $\mu_{3}$ , as shown in the figure, A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between $\mu_{1}$, $\mu_{2}$  and $\mu_{3}$ , it takes one of the four possible paths 'ef', 'eg', 'eh', or 'ei'.

Match the paths in the list I  with conditions of refractive indices in list II  and select the correct answer using the codes given below the lists.

A) P:2,Q:3, R:1,S:4

B) P;1,Q:2, R:4,S:3

C) P:4,Q:1, R:2, S:3

D) P:2,Q:3, R:4,S:1

Option D

### Explanation:

for e → i

$45^{0}>\theta_{c}$

$\sin 45^{0}>\sin\theta_{c}$

$\frac{1}{\sqrt{2}}>\frac{\mu_{2}}{\mu_{1}}$

$\mu_{1}> \sqrt{2\mu_{2}}$

For e $\rightarrow$ f

angle of refraction is lesser than angle of incidence , so   $\mu_{2}> \mu_{1}$ and $\mu_{2}> \mu_{3}$

for e $\rightarrow$  g $\mu_{1}= \mu_{2}$

for e  $\rightarrow$  h  , $\mu_{2}< \mu_{1}$ <  $\sqrt{2}\mu_{2}$ and   $\mu_{2} >\mu_{3}$