Question

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

Answer 1

Distance between the image (screen) and the object, D = 90cm
Distance between two locations of the convex lens, d = 20cm
The focal length of the lens = f
Focal length is related to d and D as:
$f=\frac{D^2-d^2}{4D}$
=$\frac{(90)^2-(20)^2}{4\times 90}$= $\frac{770}{36}$= 21.39cm
Therefore, the focal length of the convex lens is 21.39cm.