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

The correct option is B $15cm$

Let us assume the focal length of the lens is f

According to sign conventions,

Object distance (u) = -(f+9)

Image distance (v) = (f+25)

We know the formula

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

Substituting the values in the above formula,

$\Rightarrow \frac{1}{f}=\frac{1}{(f+25)}-\frac{1}{-(f+9)}=\frac{f+9+f+25}{(f+25)(f+9)}=\frac{2f+34}{f^2+34f+225}$

$\Rightarrow \frac{1}{f}=\frac{2f+34}{f^2+34f+225}$

$\Rightarrow 2f^2+34f=f^2+34f+225$

$\Rightarrow f^2=225$

$\Rightarrow f=15\text{cm}$

The focal length of the lens is 15 cm.