The focal length of a plano convex lens is f and its refractive index is 1.5. It is kept over a plane glass plate with its curved surface touching the glass plate. The gap between the lens and the glass plate is filled by a liquid. As a result, the effective focal length of the combination becomes 2f. Then the refractive index of the liquid is

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1.5

1.25

1.33

answer is C.

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Detailed Solution

According to lens maker’s formula The focal length of plane convex lens is $\frac{1}{f} = (n - 1) (\frac{1}{\infty} - \frac{1}{- R})$

$\frac{1}{f} = (\frac{3}{2} - 1) (\frac{1}{R}) = \frac{1}{2 R} or R = \frac{f}{2} \dots . (i)$ The focal length of liquid lens is $\frac{1}{f_{1}} = (n_{1} - 1) (\frac{1}{- R} - \frac{1}{\infty})$

$\frac{1}{f_{1}} = - \frac{(n_{1} - 1)}{R} \frac{1}{f_{1}} = - \frac{2 (n_{1} - 1)}{f}$ [Using (i)]

Effective focal length of the combination is $\frac{1}{2 f} = \frac{1}{f} + \frac{1}{f_{1}}$

$\frac{1}{2 f} = \frac{1}{f} = - \frac{2 (n_{1} - 1)}{f} \Rightarrow 2 (n_{1} - 1) = 1 - \frac{1}{2} = \frac{1}{2} \Rightarrow n_{1} - 1 = \frac{1}{4} \Rightarrow n_{1} = \frac{5}{4} = 1.25$