Question

The 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 distance from the mirror than the object. The magnification of the image is

• A. $\frac{8}{3}$
• B. $2.5$
• C. $2$
• D. $-1.5$

Answer 1

The correct option is D $-1.5$

In concave mirror image always formed in the same side of object.
Let $u=x$
$v=10+x$
From mirror formula
$f=\frac{uv}{u+v}$

Substituting $u$ and $v$,
$x^2-14x-120=0$

$\Rightarrow x=20,-6$

Since $x$ is positive, $x=20$

Therefore, $u=20,v=30$

Magnification $m=-\frac{v}{u}=-1.5$