Question

When an object is at a distance $u_{1}$ and $u_{2}$ from a lens, real image and a virtual image is formed respectively having same magnification. The focal length of the lens is

• A. $u_{1}-u_{2}$
• B. $\frac{u_{1}-u_{2}}{2}$
• C. $\frac{u_{1}+u_{2}}{2}$
• D. $u_{1}+u_{2}$

Answer 1

Answer: (C)

$m=\frac{f}{f+u}$
For real image
For virtual image
$-m=\frac{f}{f-u_{1}}, +m=\frac{f}{f-u_{1}}, $
$-\frac{f}{f-u_{2}}=\frac{f}{f-u_{1}} $
$\Rightarrow f=\frac{u_{1}+u_{2}}{2}$