Question

A $3cm$ tall object is placed at a distance of $7.5cm$ from a convex mirror of focal length $6cm.$ Find the location, size and nature of the image.

Answer 1

Given,

Height of object, $h_0=3cm$

Object distance, $u=7.5cm$

Focal length, $f=6cm$

from mirror formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{6}=\frac{1}{v}-\frac{1}{7.5}$

$\frac{1}{v}=\frac{1}{6}+\frac{1}{7.5}$

$v=3.33cm$

magnification, $m=\frac{h_i}{h_0}=-\frac{v}{u}$

$\Rightarrow$ $\frac{h_i}{3}=\frac{-3.33}{-7.5}$

$\Rightarrow$ $h_i=1.332cm$

Image will be $3.33cm$ on the right side of the mirror and will be virtual.

Height of the image will be $1.332cm$