Question

A concave mirror forms an image of 20 cm high object on a screen placed 5.0 m away from the mirror. The height of the image is 50 cm. Find the focal length of the mirror and the distance between the mirror and the object.

Answer 1

Given that, $h_1=20\text{dm}$

v = -5 m = -500 cm,

Since $\frac{-v}{u}=\frac{h_2}{h_1}$

or $\frac{500}{u}=\frac{50}{20}$

(because the image is inverted)

or $u=-500\times \frac{2}{5}$

= - 200 cm = -2 m

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

or $\frac{1}{-5}+\frac{1}{-2}=\frac{1}{f}$

or $-\frac{1}{f}=\frac{7}{10}$

or $f=-\frac{10}{7}=-1.44$

So, the focal length is 1.44 m.