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

A pin is placed 10cm in front of a convex lens of focal length 20cm an

1.	A pin is placed 10cm in front of a convex lens of focal length 20cm and refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature of 22cm. Determine the position of the final image. Is the image real or virtual.
Answer» Solution :As radius of curvature of silvered surface is 22cm, so `f_M=R/2=(-22)/2=-11cm` and Hence `P_M=-1/ f_M=- 1/(-0.11)=1/0.11 D` Further as the focal length of lens is 20cm, i..E, 0.20m its power will be given by `P_L=-1/f_L=1/0.20 D` Now as in image formation, LIGHT after passing through the lens will be reflected back by the curved MIRROR through the lens again. `P=P_L+P_M+P_L=2P_L+P_M` i..e., `P=2/0.20+1/0.11=210/11 D` So the focal length of equivalent mirror `F=-1/P=-11/210 m=-110/21 cm` i..e, the silvered lens behaves as a concave mirror of focal length `(110//21) cm`. SO for object at a distance 10cm in frontof it `1/v+1/(-10)=- 21/110` i..e, `v=-11cm` i..e, image will be 11cm in FRONT of the silvered lens and will be real as SHOWN in figure.