Question

The real image of an object placed on the principal axis of a concave mirror of focal length 12 cm is formed at a point which is 10 cm more distant from the mirror than the object. The magnitude of magnification of the image is:

• A. 2
• B. 1.5
• C. 1
• D. 2.5

Answer 1

The correct option is B 1.5

Since the mirror is concave, focal length is $f=-12cm$
Let u be the object distance and v be image distance.

Using mirror formula,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{-12}\cdots \left(i\right)$

Given, image is 10 cm more left than the object. Image distance is:
$v=u-10\cdots \left(ii\right)$

Substituting (ii) in (i), we get:
$\frac{1}{u}+\frac{1}{u-10}=\frac{1}{-12}$
$\frac{u-10+u}{(u-10)u}=\frac{1}{-12}$
Simplifying, we get
$u^2+14u-120=0$
$u=\{-20cm,6cm\}$

Object distance cannot be positive.
$u=-20cm$

Image distance is:
$v=u-10=-30cm$

Magnification is given by:
$m=\frac{-v}{u}$
$m=\frac{-(-30)}{-20}$
$m=-1.5$

Magnitude of magnification is:
$|m|=1.5$