A pin is placed 10cm in front of a convex lens of focal length 20cm, made of a material having refractive index 1.5 . The surface of lens farther away from the pin is silvered and has a radius of curvature 22cm. Determine the position of the final image. Is the image real or virtual?

Options

A. 11cm, virtual
B. 11 cm, ral
C. 21 cm, virtual
D. 21 cm, real

Answer

B

Explanation

`(1)/(F)=(1)/(f_l)+(1)/(f_m)+(1)/(f_l)`
`(2)/(f_l)+(1)/(f_m)=(2)/(20)+(1)/((22)/(2))=(1)/(10)+(1)/(11)`
`=(21)/(110)`
The silvered lens behaves as concave mirror of focal length `(110)/(21)cm`
`(1)/(v)+(1)/(u)=(1)/(f)`
`(1)/(v)+(1)/(-10)=(1)/((-110)/(21))`
`(1)/(v)=(1)/(10)-(21)/(110)=(11-21)/(110)=-(1)/(11)`
`v=-11cm`, real image