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?

Answer

A, C

Explanation

The focal length of the equivalent mirror is
`(1)/(F)=(2)/(f)+(1)/(f_(m))`
`=(2)/(20)+(2)/(22)=(1)/(10)+(1)/(11)=(21)/(110)`
impliesF=(110)/(21)`
NOTE: Since the focal length is positive it is a converging mirror
Now, `(1)/(u)+(1)/(v)=(1)/(f)implies(1)/(-10)+(1)/(v)=(1)/((-110)/(21))` implies`(1)/(v)=(1)/(10)-(21)/(110)impliesv=-11cm`
NOTE: The negative sign indicates the image is real.