A screen is placed at a distance of 90 cm from an object. The image of the object on the screen is formed by a convex lens placed at two different locations separated by 20 cm. The focal length of the lens is approximately

21.4 cm

The correct answer is Option (3) → 21.4 cm

Given:

Distance between object and screen: $D = 90\ \text{cm}$

Distance between two lens positions: $d = 20\ \text{cm}$

For lens forming real image on screen at two positions, lens formula gives:

Focal length: $f = \frac{D^2 - d^2}{4D}$

Substitute values:

$f = \frac{90^2 - 20^2}{4 \cdot 90} = \frac{8100 - 400}{360} = \frac{7700}{360} \approx 21.39\ \text{cm}$

∴ Focal length of the lens ≈ 21.4 cm