An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object, find the radius of curvature of the convex mirror.

Given: An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object,

To find the radius of curvature of the convex mirror.

Solution:

As per the given criteria,

object distance from the convex mirror, $u=36cm$

distance of plane mirror from the object, $d=24cm$

So,

The distance of plane mirror from the convex mirror will be

$34-12=12cm$

The image formed by the plane mirror will be at a distance of 24cm from the plane mirror and 12 cm from the convex mirror.

Since both the images should coincide therefore the convex mirror will form image at a distance of 12cm from itself.

Therefore, $u=-36cm$

$v=12cm$

Applying the lens formula, we get

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}⟹\frac{1}{f}=\frac{1}{12}+\frac{1}{(-36)}⟹\frac{1}{f}=\frac{3-1}{36}⟹f=18cm$

And we know the radius of curvature, $R=2f=2\times 18=36cm$