A point object is placed at distance of 20 cm from a thin plane - convex lens of focal length 15 cm . The plane surface of the lens is now silvered . The image created by the system is :-

Options

A. 60 cm to the right of the lens
B. 30 cm to the left of the lens
C. 24 cm to the right of the lens
D. 12 cm to the left of the lens

Answer

D

Explanation

The effective focal length of the silvered lens is given by
`(1)/(F)=(2)/(f)+(1)/(f_(m))=(2)/(15)+(1)/(oo)=(2)/(15)`
which gives `F=(15)/(2)` cm. The silvered lens behaves like a concave mirror. Using the spherical mirror formula `(1)/(v) +(1)/(u)=(1)/(F)`, we have
(`:' `u = -20 cm and F = -15/2 cm)
`(1)/(v)+(1)/(-20)=(2)/(-15)`
which gives v = -12 cm. The negative sign indicates that the image is formed to the left of the lens.