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

Q. If the convex lens is replaced by a glass plate of thickness 6cm, refractive index `mu=(3)/(2)` and gives rise to an image coincident with itself, then the value of d is equal to

Options

A. 20cm
B. 30cm
C. 40cm
D. 60cm

Answer

a.

Explanation

Shift produced by the glass plate
`Deltax=(1-(1)/(mu))t=(1-(2)/(3))6=2cm`
For the mirror, the object is placed at a distance
`[12+6+d-Deltax]=(16+d)`
The image is coincident with the object itself if
`(16+d)=36cmrArrd=20cm`