A convex lens of focal length 40cm is held at a distance 12cm coaxially above a concave mirror of focale length 18cm.

Q. A luminous point object placed d cm above the lens on its axis gives rise to an imag coincident iwth itself, then the value of d is equal to

Options

A. 15cm
B. 30cm
C. 24cm
D. 18cm

Answer

a.

Explanation

Since final image will coincide with the object if the ray retraces its path after reflection from the concave mirror, i.e., the ray strike the mirror normally. The normal rays at the mirror after being extended must pass through the center of curvature of the mirror for the refraction at the convex lens
`v=(2f-12)=24cm`
`u=d`
`(1)/(-24)-(1)/(-d)=(1)/(40)`
`(1)/(d)=(1)/(400)+(1)/(24)=(3+5)/(120)`
`d=15cm`