A small object is placed 50 cm to the left of a thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle θ=30∘ to the axis of the lens, as shown in the figure.
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates (in cm) of the point (x,y) at which the image is formed are
(A)(0,0)
(B)(50−253,25)
(C)(25,253)✓ Correct
(D)(125/3,25/3)
Answer: (C)
Solution
For the lens: v1−−501=301, giving v=75 cm (to the right of lens).
This image acts as object for the mirror at 25 cm from it. With focal length f=50 cm: v′1+−251=501, giving v′=−50 cm (50 cm to the left of mirror, i.e., at the lens position if mirror were not tilted).
When mirror is tilted by 30°, the reflected ray rotates by 60°. The image point moves from the lens position along a direction making 60° with the axis.
Distance = 50 cm, so: x=50cos60°=25 cm y=50sin60°=253 cm
JEE Advanced · 2016 · 22 May 2016 · Paper 2 · Single correct option
