Question

An object is kept at a distance of $4cm$ from the first focus of a convex lens. A real image is formed at a distance of $9cm$ from its second focus. Then focal length of that lens is

• A. $6.5cm$
• B. $13cm$
• C. $6cm$
• D. $36cm$

Answer 1

Answer: (C)

$6cm$

Since it is an equiconvex lens $f_1=f_2$

$u=-\left(4+f\right)$

$v=9+f$

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

$\Rightarrow \frac{1}{f}=\frac{1}{9+f}+\frac{1}{4+f}=\frac{2f+13}{f^2+13f+36}$

$\Rightarrow 2f^2+13f=f^2+13f+36$

$\Rightarrow f^2=36$

$\Rightarrow f=\pm 6cm$

Hence the correct answer is option (C).