Question

A needle placed at $30cm$ from the lens forms an image on a screen placed $60cm$ on the other side of the lens. Identify the type of lens and determine the focal length.

Answer 1

Given,

The needle is placed at $30cm$ from the lens, it forms an image on a screen placed at $60cm$ on the other side of the lens.

Object distance, $u=-30cm$

Image distance, $v=60cm$

Focal length, $f$

Applying lens formula,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}⟹\frac{1}{f}=\frac{1}{60}-\frac{1}{-30}⟹\frac{1}{f}=\frac{1+2}{60}⟹f=20cm$

Since the image is formed on the other side of the lens, the image is real. also, the focal length is positive. So, it is a convex lens.