Question

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it

• A. 30 cm
• B. 60 cm
• C. 50 cm
• D. 12 cm

Answer 1

Answer: (C)

In order to obtain image coincident with object, the image of object after refraction from the convex lens must be formed on the center of curvature of the convex mirror.

Distance of image from convex lens after refraction from it can be found by using lens equation:

$\Rightarrow \frac{1}{v}=\frac{1}{u}+\frac{1}{f}=\frac{1}{-30}+\frac{1}{20}$

$\Rightarrow v=60cm$

Thus, image is formed at a distance of $60cm$ from the lens.

Thus, the convex mirror should be kept at distance $60cm-10cm=50cm$ from the lens such that the image is formed at its center of curvature.