Question

An object placed at a distance of 16 cm from first principal focus of convex lens, produces a real image at a distance of 36 cm from its second principal focus. Then the focal length of the lens is :

• A. $9cm$
• B. $25cm$
• C. $24cm$
• D. $17cm$

Answer 1

Answer: (C)

$24cm$

Let focal length of the lens be $f$,

Given,

Object distance $=16+f=u$

Image distance $=36+f=v$

Distance of 1st and 2nd principal focus is same from the optical centre

From, lens formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f}=\frac{1}{36+f}+\frac{1}{16+f}$

$\frac{1}{f}=\frac{16+f+36+f}{(36+f)(16+f)}$

On solving

$f=24cm$