Question

A real object is at a distance of 1m from its virtual image by a diverging lens. Determine the focal length of the lens if magnification is 0.6 :-

• A. $-3.25m$
• B. $-2.5m$
• C. $-3.75m$
• D. $-1.25m$

Answer 1

The correct option is A $-3.25m$

$m=\frac{v}{u}=0.6-\left(2\right)$

As the iniage is virtual \& lens is diverging both

object \& image are at same side.

: by fig we canbee that $\to v+1=u$ -(1)

by lens formula $\to$

$\begin{array}{cc}& \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \Rightarrow & \frac{1}{v}-\frac{y}{v+y}=\frac{1}{f}\\ \Rightarrow & \frac{1}{(-1.5)}\frac{1}{(-2.5)}=\frac{1}{f}\end{array}$

$V=0.6\mu \left(by\right(2)$

putting it in (1)

$0.6\mu +1=\mu$

$\frac{1}{0.4}=\mu$

$[u=2.5m]$

$[V=1.5m]$

by solving we get $[f=\frac{-15}{4}]\therefore f=-3.25m$

Hence option $A$ is correet.