Question

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

• A. $v=8.57cm$, $hi=2.14cm$
• B. $v=40cm$, $hi=5cm$
• C. $v=57cm$, $hi=14cm$
• D. $v=4cm$, $hi=2.14cm$

Answer 1

The correct option is A $v=8.57cm$, $hi=2.14cm$

Given,
Object distance $u=-20cm$
Object height $h_o=5cm$
Radius of curvature $R=30cm$
We know $f=R/2=15cm$

Mirror formula
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{-20}=\frac{1}{15}$

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

$v=8.57cm$

Image is virtual and erect and formed behind the mirror.
$m=-v/u$
$m=hi/ho$
$hi/5=8.57/20$
$hi=0.428\times 5=2.14cm$