Question

An object `50 cm` tall is placed on the principal axis of a convex 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, `h_(1) =50cm, h_(2)= -20cm, v=10cm, f=?`
As image is formed on the screen, it must be real and inverted. That is why `h_(2)` is negative.
From `m =(h_(2))/(h_(1))=v/u, (-20)/(50)=(10)/(u)` or `u = (-50 xx10)/(20)= -25 cm`
Using lens formula, `(1)/(f) = (1)/(v) - 1/u`
`(1)/(f)= 1/10 - 1/-25 = (5+2)/(50) =7/50` or `f=50/7 cm =7.14cm`