Question

An object of height 5 cm is placed at 30 cm distance on the principal axis infront of a concave mirror of focal length 20 cm. Find the image distance and size of the image.

Answer 1

Height of object, $h_o=5cm$, object distance $u=-30cm$, focal length $f=-20cm$

Now, from mirror formula :$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

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

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

$=-\frac{1}{60}$

$v=-60cm$ - image distance

Magnification, $m=-\frac{v}{u}=-\frac{-60}{-30}=-2$

Size of image, $h_i=m\left(h_o\right)=-2\left(5\right)=-10cm$