A double convex lens of focal length 30 cm is made of glass of refractive index 1.6. When it is immersed in a liquid, the focal length is found to be 126 cm. The refractive index of the liquid is

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1.33

1.4

1.42

1.5

answer is B.

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Detailed Solution

$\frac{1}{f} = [\frac{μ_{2}}{μ_{1}} - 1] [\frac{1}{R_{2}} - \frac{1}{R_{1}}]$

$\frac{1}{30} = [1.6 - 1] [\frac{1}{R_{2}} - \frac{1}{R_{1}}] \Rightarrow [\frac{1}{R_{2}} - \frac{1}{R_{1}}] = \frac{1}{30 \times 0.6}$

In liquid:

$\frac{1}{126} = [\frac{1.6}{x} - 1] [\frac{1}{30 \times 0.6}] = \frac{1}{7} + 1 = \frac{1.6}{x}$

$\Rightarrow \frac{8}{7} = \frac{1.6}{x}$

$\Rightarrow x = 1.4$

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