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Q.

Two identical glass $(μ_{g} = \frac{3}{2})$ equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water $(μ_{w} = \frac{4}{3})$ . The focal length of the combination is

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a

$\frac{f}{3}$

b

$\frac{4 f}{3}$

c

$\frac{3 f}{4}$

d

f

answer is D.

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Detailed Solution

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Let us apply lens maker’s formula for convex lens.
$\begin{array}{l} \frac{1}{f} = (1.5 - 1) \frac{2}{R} \\ \frac{1}{f} = \frac{1}{R} \dots \dots \dots \dots . . (1) \end{array}$
For liquid lens
$\begin{array}{l} \frac{1}{f^{'}} = - (\frac{4}{3} - 1) \frac{2}{R} \\ \frac{1}{f^{'}} = - \frac{2}{3 R} \dots (2) \\ \frac{1}{f^{'}} = - \frac{2}{3 f} ∵ \frac{1}{f} = \frac{1}{R} \end{array}$

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