Question

A concave mirror of focal length 20cm is placed 50 cm from a wall. How far from the wall an object be placed to form its real image on the wall?

Answer 1

Explanation: V=-50 cm F=-20cm

From mirror formula 1/u = 1/f – 1/v  

= -1/20+ 1/50 =-3/100 U = -33.3 cm

Therefore the distance of the object from the wall x = 50 – u  

X = 50 – 33.3 = 16.7 cm.

Answer 2

Given

Focal length, f = -20cm (concave mirror)

Object distance i.e distance of the wall from the mirror, v = -50cm

We have to find v (image distance)

By applying mirror's formula

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

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

$\mathsf{\frac{1}{u} = \frac{1}{-20} - (\frac{1}{-50})}$

$\mathsf{\frac{1}{u} = \frac{1}{-20} + \frac{1}{50}}$

$\mathsf{\frac{1}{u} = \frac{-5 + 2}{100}}$

$\mathsf{\frac{1}{u} = \frac{-3}{100}}$

$\mathsf{u = \frac{-100}{3}}$

$\fbox{\mathsf{u = -33.3 cm}}$

Distance of the object from the wall (x) = 50 – u

X = 50 – 33.3 = 16.7 cm.

The object is to be placed at 16.7 cm from the mirror to form its real image on the wall