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A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. it is immerse in 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

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1.21

1.26

1.36

1.42

answer is C.

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Detailed Solution

Applying Snell’s law at point P
$n_{1} \sin θ = n_{2} \sin 90^{\circ} \sin θ = \frac{11 .54 / 2}{\sqrt{10^{2} + (11 .54 / 2)^{2}}}$

refractive index of liquid = 2.72
$∴ n_{2} = 2 .72 \times \frac{11 .54 / 2}{\sqrt{(10)^{2} + {(\frac{11 .54}{2})}^{2}}} ∴ n_{2} = 1 .36$

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