Question

An object placed at a distance of $9cm$ from first principal focus of convex lens, produces a real image at a distance of $25cm$ from its second principal focus. Then focal length of lens is:

• A. $9cm$
• B. $25cm$
• C. $15cm$
• D. $17cm$

Answer 1

The correct option is C $15cm$

It focal length be $f$ then

$u=-(f+a)$

$v=+(25+f)$

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

$\Rightarrow \frac{1}{f}=\frac{1}{25+f}-\frac{1}{-(f+9)}=\frac{f+9+f+25}{(f+9)(f+25)}=\frac{2f+3f}{(f+4)(f+25)}$

more solving $(f+9)(f+25)=2(f+17)f$

$f^2+25f+9f+225=2f^2+34f$

$f^2=225\Rightarrow f=15cm$