An object is placed at $25 c m$ in front of a convex lens. Its image is formed at $50 c m$ from the lens on the same side as the object. Find the power of the lens.

1 D

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2 D

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3 D

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4 D

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Solution

The correct option is B $2 D$
Given:
Object distance, $u = - 25 c m = - \frac{25}{100} m$
Image distance, $v = - 50 c m = - \frac{50}{100} m$
Let the focal length of the lens be $f$ , and its power be $P$ .
Using the lens formula:
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} = P$
Here, $v, u$ and $f$ should be in metres.
$P = \frac{1}{(- 50 / 100)} - \frac{1}{(- 25 / 100)}$
$P = \frac{100}{- 50} + \frac{100}{25} = 100 \times (\frac{1}{25} - \frac{1}{50})$
$P = 100 \times \frac{1}{50} = 2$
$P = 2 D$
The power of the given lens is $2 D$ .

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