Question

A candle is placed at 60 cm from the pole of a concave mirror with focal length of 20 cm. Find the distance at which the image is ​formed and hence magnification.​

• A. 15 cm, m = -0.5​
• B. 30 cm, m = -0.5​
• C. 30 cm, m = +0.5​
• D. 15 cm, m = +0.5​

Answer 1

The correct option is B 30 cm, m = -0.5​

Given,

u = object distance = - 60 cm

f = focal length = - 20 cm

Using the mirror formula,

$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\frac{-1}{60}+\frac{1}{v}=\frac{-1}{20}$
$\frac{1}{v}=\frac{1}{60}+\frac{-1}{20}$

v = - 30 cm

• We get image distance (v) = - 30 cm.

• Now the question is asking for the distance of the image from the mirror which will be simply the magnitude of image distance i.e. 30 cm.

• Hence the image will be formed at 30 cm from the mirror.

• Now, magnification(m) can be calculated using,

m = - v/u = -(-30)/(-60) = -½ = -0.5

• Thus, the correct answer is option B.