Question

A convex lenses of focal length 40 cm is held coaxially 12 cm above a concave mirror of focal length 18 cm. An object held x cm above the lens gives rise to an image coincident with it. The x is equal to

• A. 12 cm
• B. 15 cm
• C. 18 cm
• D. 30 cm

Answer 1

The correct option is B 15 cm

For the final image to be coincident with the object, the rays must retrace their path after reflection from the concave mirror. Hence the image obtained after first refraction from the convex lens must lie on the radius of curvature of the lens.

Hence the distance of image from the lens $=R-13cm=2\left(18\right)cm-12cm=24cm$

Using lens equation,

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

$\frac{1}{-24}-\frac{1}{-x}=\frac{1}{40}$

$⟹x=15cm$