Question

When the object is at distance $u_1$ and $u_2$ from a lens, a real image and virtual image are formed respectively having the 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

The correct option is C $\frac{u_1+u_2}{2}$

Based on the info given, the magnification produced will be, $m$ and $-m$

Hence,

$u_1=f(1+\frac{1}{m})$

$u_2=f(1-\frac{1}{m})$

Eliminating $m$ from the 2 equations we get,

$f=$ $\frac{u_1+u_2}{2}$