Question

An object $5.0cm$ in length is placed at a distance of $20cm$ in front of a convex mirror of radius of curvature $30cm$. Find the position of the image, its nature, and its size.

Answer 1

Given: $u=-20cm$

$f=R/2=15cm$

Size of image, $h=5cm$

Let size of image be $h^{\prime }$

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

$\frac{1}{-20}+\frac{1}{v}=\frac{1}{15}$

$v=\frac{60}{7}=8.57cm$

The image is formed $8.57cm$ behind the mirror. It is virtual and erect.

Magnification, $m=-v/u=8.57/20=0.428$

Also, $m=h^{\prime }/h=h^{\prime }/5$

From above, $h^{\prime }/5=0.428$

$h^{\prime }=2.14cm$