Question

A converging lens of focal length $20cm$ forms an image, when an object is placed $15cm$ away from it. Calculate how far (in cm) the image is, from the lens. Include the sign.

• A. -60

Answer 1

The correct option is A -60
Given:
A converging (convex) lens of focal length $20cm$.
A convex lens has a positive focal length, hence, the focal length $f=+20cm$
The object distance is always negative, $u=-15cm$
Since, the object is placed at a distance smaller than the focal length, i.e. between the focus and the optic centre, the image formed would be virtual, erect and enlarged in nature.
Also, the image forms on the same side of the lens.
Applying the lens equation, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$\frac{1}{20}=\frac{1}{v}-\frac{1}{(-15)}$
$⟹\frac{1}{v}=\frac{1}{20}-\frac{1}{15}=\frac{-1}{60}$
$⟹v=-60cm$
Image distance = $-60cm$