Question

An object of size 3 cm is placed at 30 cm in front of a concave mirror of radius of curvature 40 cm. Find the distance and size of image from the mirror and describe the nature of the image

Answer 1

Given,

Radius of curvature, $R=40cm$

Object distance, $u=30cm$

Object height, $h_o=3cm$

The focal length of the mirror=$f=-\frac{R}{2}$

$=-20cm$

From mirror equation,

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

$⟹\frac{1}{v}+\frac{1}{-30}=\frac{1}{-20}$

$⟹v=-60cm$

The magnification, $M=\frac{-v}{u}$

$=-\frac{-60}{-30}$

$=-2$

Hence the image is inverted, enlarged, real and its size is $2\times 3cm=6cm$.