A point object is placed at distance 60cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to principal axis of lens and at distance 40cm from it the final image would be formed at distance of:

Options

A. 30 cm from the lens, it would be a real image
B. 30 cm from the plane mirror, it would be a virtual image
C. 20 cm from the plane mirror, it would be a virtual image
D. 20 cm from the lens, it would be a real image

Answer

C

Explanation

20 cm from the plane mirror, it would be a virtual image,
First, for image formation from lens
u = −60cm , f = +30cm
`rArr v = (uf)/(u + f) = (-60 xx 30)/(- 60 + 30) 60 ` cm
this real image formed by lens acts as virtual object for mirror

Real image from plane mirror is formed 20 cm in front of mirror, hence at 20 cm distance from lens. Now, For second refraction from lens, u = −20cm , f = +30cm
`v = (uf)/(u + f) = (-20 xx 30)/(-20 + 30) 60 cm `
So, Final virtual image is 60 cm from lens, or 20 cm behind mirror.