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?

Explanation

`f_l=20cm`
`(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)`
`F=(110)/(21)` cm
The silvered lens will behave as concave mirror of focal length `(110)/(21)` cm.
`(1)/(v)+(1)/(-10)=(1)/((-110)/(21))`
`(1)/(v)=(1)/(10)-(21)/(110)=(11-21)/(110)`
`v=-11cm`
Distance of image is 11 cm left of silvered lens/mirror. Image is real.