Question

At what distance from a convex mirror of focal length 2.5 m should a boy stand so that his image has a height equal to half the original height?

• A. $2.5m$ from the mirror
• B. $5m$ from the mirror
• C. $7.5m$ from the mirror
• D. $10m$ from the mirror

Answer 1

The correct option is A $2.5m$ from the mirror

Given,

The focal length of mirror is $f=-2.5m$

The image height is half the object height , hence if object height is $h$ then

Image height $h^{\prime }=\frac{h}{2}$

Therefore the magnification is given as

$m=\frac{h^{\prime }}{h}=\frac{1}{2}$

Also the magnification is given as

$m=\frac{-v}{u}\Rightarrow \frac{1}{2}=\frac{v}{u}\Rightarrow v=\frac{-u}{2}$

Now applying mirror formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\Rightarrow \frac{1}{-2.5}=\frac{-2}{u}+\frac{1}{u}$

$\frac{1}{2.5}=-\frac{1}{u}\Rightarrow u=-2.5m$

Hence object has to be placed at $2.5m$ from the mirror.