Optics 2 Question 5

5. A point source $S$ is placed at the bottom of a transparent block of height $10 mm$ and refractive index 2.72 . It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter $11.54 mm$ on the top of the block. The refractive index of the liquid is

(2014 Adv.)

(a) 1.21

(b) 1.30

(c) 1.36

(d) 1.42

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Answer:

Correct Answer: 5. (c)

Solution:

  1. At point $Q$ angle of incidence is critical angle $\theta _C$, where

$$ \sin \theta _C=\frac{\mu _l}{\mu _{\text {block }}} $$

In $\triangle P Q S, \sin \theta _C=\frac{r}{\sqrt{r^{2}+h^{2}}}$

$\therefore \quad \frac{\mu _l}{\mu _{\text {block }}}=\frac{r}{\sqrt{r^{2}+h^{2}}}$

$\Rightarrow \quad \mu _l=\frac{r}{\sqrt{r^{2}+h^{2}}} \times 2.72$

$$ =\frac{5.77}{11.54} \times 2.72=1.36 $$



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