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Question:

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 titled 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:

(0,0)

(25,25√3)

(125/3,25/√3)

(50√3,25)

Solution:

Let final image be at a distance x from the lens to its right and between the lens and the mirror.
y50−x=tan60°=√3
y+√3x=50√3
This is satisfied by option A and D.
A and B both option satisfy this,
Size of image > Size of object
√y²+(50−x)²sin30°>25sin30°
y²+(50−x)²>625
Checking option D, 625(3)+625=4(625)>625
Answer is option D.