Question

An object is placed 20 cm in front of a plano convex lens of focal length 15 cm. The plane surface of the lens is silvered. The image will be formed at a distance

• A. 60 cm to the left of the lens
• B. 60 cm to the right of the lens
• C. 12 cm to the left of the lens
• D. 12 cm to the right of the lens.

Answer 1

The correct option is C 12 cm to the left of the lens

consider the arrangement to be of combination of plano convex lens and plane mirror .the light ray from the object strikes the plano convex lens and let the distance of first image be at $v1$

$u=-20$

$\frac{1}{v1}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v1}+\frac{1}{20}=\frac{1}{15}$

$\frac{1}{v1}=-\frac{1}{20}+\frac{1}{15}$

$\frac{1}{v1}=\frac{1}{60}$

$v1=60$

this image serves as virtual object for the mirror and a real image is formed at a distance 60cm to the left of mirror and intrn this serves as virtual object for the plano convex lens

$u=+60f=+15$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}-\frac{1}{60}=\frac{1}{15}$

$\frac{1}{v}=\frac{1}{12}$

$v=+12$

i.e. final image is formed to the left of lens at a distance 12cm , hence option $C$ is correct