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.

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:

f² = (D²-d²)/4D

= [(90)² – (20)²]/ (4 x 90) = 770 /36 = 21.39 cm

Therefore, the focal length of the convex lens is 21.39 cm