Question

A concave mirror of focal length 20 cm produces an image twice the height of the object.if the image is real,then distance of the object from the mirror is

1. 20cm.

2. 60cm.

3. 10cm.

4. 30cm

Answer 1

Given Data:

Focal length of concave mirror, $f=-20cm$

Magnification produced by mirror, $m=-2=\frac{-v}{u}$ (since image is real)

Or, $v=2u$

Step 1: To find distance of image:

From mirror formula,

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

$\frac{1}{-20}=\frac{1}{2u}+\frac{1}{u}⟹\frac{-1}{20}=\frac{1+2}{2u}$

$\frac{-1}{20}=\frac{3}{2u}⟹u=-30cm$

So, distance of the object from mirror,

$=30cm$