Question

A $1cm$ height needle is placed at a distance of $0.1m$ from a convex mirror of focal length $0.05m$, then size of the image is

• A. $1cm$
• B. $0.66cm$
• C. $0.33cm$
• D. $0.5cm$

Answer 1

The correct option is C $0.33cm$

Object distance $u=-0.1m$

Focal length $f=0.05m$

Needle height $h_o=1cm$

Using mirror formula $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\therefore$ $\frac{1}{v}+\frac{1}{-0.1}=\frac{1}{0.05}$

$⟹v=\frac{1}{30}cm$

Object height $h_o=1cm$

Magnification $m=\frac{h_i}{h_o}=\frac{-v}{u}$

$\therefore$ $\frac{h_i}{1}=\frac{-1}{30\times (-0.1)}$

$⟹h_i=0.33cm$