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

21.4 cm

The correct answer is option (4) : 21.4 cm

If the distance between object and screen is D and distance between two positions of lens is x, then

$f=\frac{D^2-x^2}{4D}⇒f=\frac{(90)^2-(20)^2}{4\times 90}=21.38\, cm$

$≈21.4 \, cm$