Question

A candle is placed $20 \,cm$ from the surface of a convex mirror and a plane mirror is also placed so that the virtual images in the two mirrors coincide. If the plane mirror is $12 \,cm$ away from the object, what is the focal length of the convex mirror?

• A. $20\, cm$
• B. $15\, cm$
• C. $10\, cm$
• D. $5 \,cm$

Answer 1

Answer: (D)

For convex mirror, $u+v=12 \times 2=24 \,cm$
(because for plane mirror, distance of object $=$ distance of image).
Also, here for the convex mirror $u=20 \,cm$,
therefore $v=4\, cm$. Hence, using
$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
We find $f=5 \,cm$