Question

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

• A. 2
• B. - 1.5
• C. 1.5
• D. - 2

Answer 1

The correct option is B - 1.5

Given:
Focal length, $f=-12cm$
Object distance $=-u$
Image distance $\left(v\right)$ is 10 cm more than the object distance $\Rightarrow v=(u+10)$. Real images for concave mirrors are formed on the same side as the object for concave mirrors.
Using mirror formula,
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\frac{1}{-u}+\frac{1}{-(u+10)}=\frac{1}{-12}$
Simplifying,
$u^2-14u-120=0$
$u^2-20u+6u-120=0$
$(u-20)(u+6)=0$
Object distance is taken as $-u$. Hence, $u$ is positive.
$⟹u=20cm$
Hence, image distance is:
$v=-30cm$
Magnification is given by:
$m=-\frac{\text{Image Distance}}{\text{Object Distance}}$
$m=-\frac{-30}{-20}=-1.5$