Concept:Use the lens formula
f1=v1−u1 with proper sign convention for each lens separately. The image formed by the first lens acts as the object for the second lens.
Explanation:For the convex lens
L1: object distance
u=−30 cm (real object, left side), focal length
f=+10 cm.
Using
v1−u1=f1:
v1+301=101→
v1=101−301=302 →
v=+15 cm (right of
L1).
This image is 15 cm to the right of
L1. Distance between lenses is 3 cm (from figure). So image formed by
L1 is
15−3=12 cm to the left of
L2 (object for
L2). For concave lens
L2: object distance
u′=+12 cm (virtual object, since image lies to its left), focal length
f′=−10 cm.
Using
v′1−u′1=f′1:
v′1−121=10−1→
v′1=121−101=60−1 →
v′=−60 cm (negative sign means image is on the same side as the object, i.e., to the left of
L2).
Hence final image is 60 cm to the left of the concave lens.
Answer:60 cm to the left of the concave lens (Option C).