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?

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

Tardigrade Admin · Accepted Answer

For convex mirror, u+v=12 × 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 (1/v)+(1/u)=(1/f) We find f=5 cm

Q. A candle is placed $20 c m$ 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 $12 c m$ away from the object, what is the focal length of the convex mirror?

$20 c m$

$15 c m$

$10 c m$

$5 c m$

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

Q. A candle is placed 20cm 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 12cm away from the object, what is the focal length of the convex mirror?

20cm

15cm

10cm

5cm