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 thelens a convex mirror of radius of curvature 10 cm be placed in order to have an image of the object coincident with it

Options

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

Answer

C

Explanation

If image coincides with image, for this image by lens should be formed at centre of curvature of mirror.
Image by lens : `u=-30cm,v=d+10,f=20cm`
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(d+10)-(1)/(-30)=(1)/(20)`
`(1)/(d+10)=(1)/(20)-(1)/(30)=(1)/(60)`
`d+10=60impliesd=50cm`