Question

A luminous object is placed 20 cm from surface of a convex mirror and a plane mirror is set so that virtual images formed in two mirrors coincide. If plane mirror is at a distance of 12 cm from object, then focal length of convex mirror is:

• A. $-5cm$
• B. $-10cm$
• C. $-20cm$
• D. $-40cm$

Answer 1

The correct option is A $-5cm$

Mirror Equation: $\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

For plane mirror, $f=\infty$, hence $v=-u=-12cm$

Thus, there is a distance of $12-(-12)=24cm$ between object and image

For convex mirror, $u^{\prime }=20cm$ (given)

Since the images coincide, $v^{\prime }=-(24-20)=-4cm$

So $f^{\prime }={(\frac{1}{20}+\frac{1}{-4})}^{-1}={(-\frac{1}{5})}^{-1}=-5cm$