Question

An object of 2 cm height is placed at a distance of 10 cm from a concave mirror of radius of curvature 30 cm. Find the image distance, height and magnification.

Answer 1

Given that,

Focal length $f=\frac{R}{2}$

Radius of curvature $R=30$

Object distance $u=10cm$

Height of object $h_o=2cm$

From the mirror formula,

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

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

$-\frac{1}{v}=\frac{1}{10}-\frac{2}{30}$

$-\frac{1}{v}=\frac{3-2}{30}$

$v=-30cm$

Now, the magnification is

$m=\frac{-v}{u}$

$m=\frac{30}{10}$

$m=3$

Now, the height of image

$m=\frac{h_i}{h_o}$

$3=\frac{h_i}{2}$

$h_i=6cm$

Hence, the image distance is $-30cm$, height of image is $6cm$ and magnification is $3$