A point object is placed at a distance of 12cm on the axis of a convex lens of focal length 10cm . On the other side of the lens, a convex mirror is placed at a distance of 10cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of convex mirror?

A point object is placed at a distance of 12cm on the axis of a convex

1.	A point object is placed at a distance of 12cm on the axis of a convex lens of focal length 10cm . On the other side of the lens, a convex mirror is placed at a distance of 10cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of convex mirror?
Answer» Solution :For convex lens `1/v-1/(-12)=1/10` i.e., v=60 cm i.e., in the absence of convex mirror. Convex lens will FORM the image `I_1` at a DISTANCE of 60cm behind the lens. Since the mirror is at a distance of 10cm from the lens `I_1` will be at a distance of 60-10=50 cm from the mirror, i.e., `MI_1=50 cm` Now as the FINAL image `I_2` s formed at the object O itself, the rays after reflection from the mirror retraces its PATH i.e., rays on the mirror are INCIDENT normallly i.e., `I_1` is the centre of the mirror , so that `R=MI_1=50 cm and ` hence `F=(R//2)=(50//2)=25 cm`