Question

An object 50 cm tall is placed on the principal axis of a concave lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens

Answer 1

here,

height of the object, ho = 50 cm

height of the image, hi = -20 cm

the distance of the image, v = 10 cm

now, magnification formula for a lens is

m = v/u = hi/ho

so, the object distance will be

u = v.(ho/hi)

or

u = 10.(50/20)

thus,

u = -25 cm

so, the focal length will be

1/f = 1/v - 1/u

or

1/f = 1/10 + 1/25

1/f = 0.1 + 0.04

so, the focal length of the convex lens will be

f = 7.14 cm