A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

Options

A. virtual and at a distance of 16 cm from the mirror
B. real and at a distance of 16 cm from the mirror
C. virtual and at a distance of 20 cm from the mirror
D. real and at a distance of 20 cm from the mirror

Answer

B

Explanation

Focal length of the biconvex lens is 15 cm. A small object is placed at a distance of 30cm from the lens i.e. at a distance of 2f. Therefore the image should form at But since the ray strike the plane mirror before reaching `I_(1)`, The image I_(1) acts as the virtual object for reflection on plane mirror kept at a distance of 20 cm from it. It should produce an image I_(2) but as the ray encounters the lens, it gets refracted and the final image is formed at I_(3). For the last refraction from the biconvex lens, `u=10cm`.
Applying lens formuls `(1)/(v)-(1)/(u)=(1)/(f)`
`implies` `(1)/(v)=(1)/(10)=(1)/(15)` `implies` `(1)/(v)=(1)/(15)+(1)/(10)=(25)/(150)`
`implies` `v=6cm`
Therefore a real image is formed at a distance of 16cm from the plane mirror.