Question:
A screen is placed 90 cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Determine the focal length of the lens.
Solution:
Distance between the image (screen) and the object, D = 90 cm
Distance between two locations of the convex lens, d = 20 cm
Focal length of the lens = f
Focal length is related to d and D as:
$f=\frac{D^{2}-d^{2}}{4 D}$
$=\frac{(90)^{2}-(20)^{2}}{4 \times 90}=\frac{770}{36}=21.39 \mathrm{~cm}$
Therefore, the focal length of the convex lens is 21.39 cm.