Question

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

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

Answer 1

Answer: (B)

The image by the plane mirror is formed $12\, cm$ behind it. Since the two images coincide, it means image is formed $4\, cm$ behind the convex mirror. For the convex mirror, $u=-20\, cm , v = +4 \,cm$
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{4}+\frac{1}{-20}=\frac{1}{f}$
$\Rightarrow f=+5 \,cm$