The figure below shows the positions of a point object O, two lenses, a plane mirror and the final image $I$ which coincides with the object. The focal length of the convex lens is $20 c m$ . Calculate the focal length of the concave lens.

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Solution

For convex lenses $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{20} = \frac{1}{v} + \frac{1}{45}$
$\frac{1}{v} = \frac{1}{20} - \frac{1}{45}$
$v = \frac{20 \times 45}{25} = 36 c m$ .
So 'u' for concave lens = 36 - 16 = 20 cm
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{f} = \frac{1}{\infty} - \frac{1}{20}$
$f = - 20 c m$ .
So, focal length of concave lens = -20 cm.

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