Question

A convex lens and a convex mirror are separates by a distance of 10 cm such that the reflecting surface of the mirror faces the lens. The image of an object placed in front of the convex lens at a distance of 20 cm is found to coincide with the object. If the focal length of the convex lens is 15 cm, determine the focal length of the mirror.

• A. 35 cm
• B. 30 cm
• C. 15 cm
• D. 25 cm

Answer 1

The correct option is D 25 cm

Given: A convex lens and a convex mirror are separates by a distance of 10 cm such that the reflecting surface of the mirror faces the lens. The image of an object placed in front of the convex lens at a distance of 20 cm is found to coincide with the object.

To find the focal length of the mirror if the focal length of the convex lens is 15 cm

Solution:

according to the given criteria, $u=-20,f_1=15$

The position of the image formed by the convex lens

$\frac{1}{f_1}=\frac{1}{u}+\frac{1}{v}⟹\frac{1}{15}=\frac{1}{-20}+\frac{1}{v}⟹v=60cm$

The image will form at a distance of 60 cm from lens

i.e., it will be 50 cm behind the mirror, now this image will act as the virtual object for the mirror.

Also this virtual object will now coincide with the final image.

Apply mirror formula,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Substitute, $u=50cm$ and $v=50cm$

Therefore,

$\frac{1}{f}=\frac{1}{50}+\frac{1}{50}⟹f=25cm$

is the required focal length of the mirror