## Question

The focal length of a convex lens in air is 20 cm. What will be its focal length if it is immersed in a liquid of refractive index 1.35? Refractive index of glass is 1.50.

### Solution

90.8 cm

The focal length *f* of a lens in air is given by

Where *n* is refractive index of the material (glass) of the lens with respect to air. Here *f* = 20 cm, *n* = * _{a}n_{g}* = 1.50.

Let the focal length of the lens immersed in the liquid be *f**’*. Now, in the above formula, *n* will be refractive index of glass with respect to liquid. That is

*n* = _{l}n_{g}

Dividing eq. (i) by (ii), we get

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