Two identical glass (μg=32) equiconvex lenses of focal length f are kept i

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Two identical glass

(μ_{g} = \frac{3}{2})

equiconvex lenses of focal length f 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

Options:

A . f

B . f2

C . 4f3

D . 3f4

Answer: Option D
:
D
Let R be the radius of curvature of each surface. Then

\frac{1}{f} = (1.5 - 1) (\frac{1}{R} + \frac{1}{R})

∴ R = f

For the water lens

\frac{1}{f} = (\frac{4}{3} - 1) (- \frac{1}{R} - \frac{1}{R}) = \frac{1}{3} (- \frac{2}{R})

or

\frac{1}{f} = - \frac{2}{3 R}

Now using

\frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}

we have

\frac{1}{F} = \frac{1}{f} + \frac{1}{f} + \frac{1}{f}

= \frac{2}{f} - \frac{2}{3 f} = \frac{4}{3 f}

∴ F = \frac{3 f}{4}

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