An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is _____ cm.

The plane mirror forms an image at the same distance behind the mirror as the object is in front of it.

Given :

• Distance between lens and mirror = 20 cm

• Image formed by mirror = 5 cm behind the mirror

Therefore, the image formed by the lens must be 5 cm in front of the mirror.

So,

20 − 5 = 15 cm

Using lens formula :

1/f = 1/v − 1/u

For convex lens :

f = 10 cm, v = 15 cm

Substituting :

1/10 = 1/15 − 1/u

1/u = 1/15 − 1/10

1/u = (2 − 3)/30

1/u = −1/30

u = −30 cm

Negative sign shows that the object is on the left side of the lens.

Hence, the distance of the object from the lens is

30 cm