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 -​

Answer 1

The focal length of the convex mirror is 5cm.

Distance of the object from the convex mirror = −20cm (Given)

Distance from the object - 12cm (Given)

Distance of the image = v = 4cm (Given)

Focal length is represented as -

1/f = 1/v + 1/u

1/f = 1/4 + 1/−20

1/f = 5−1/20

f = 20/4

f = 5

Therefore, the focal length of the convex mirror is 5cm.

Answer 2

Focal length of the convex mirror = 5 cm

Explanation:

Given distance of the object from the convex mirror = u  = -20 cm

distance of the image from the convex mirror = v = 4 cm

We can get the focal length using the formula:

1/ f  = 1/ v + 1/ u

1/ f = 1 / 4 - 1 / 20

1/ f = 5 / 20 - 1 / 20

1/ f = 4 / 20

So focal length = 20 / 4 = 5 cm