Optics 3 Question 11

11. A small object is placed 50cm to the left of a thin convex lens of focal length 30cm. A convex spherical mirror of radius of curvature 100cm is placed to the right of the lens at a distance of 50cm. 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.

(2016 Adv.)

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) (125/3,25/3)

(b) (50253,25)

(c) (0,0)

(d) (25,253)

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Answer:

Correct Answer: 11. (d)

Solution:

For Lens

1v1u=1fv=ufu+fv=(50)(30)50+30=75

For Mirror

1v+1u=1fv=ufufv=2532(50)253250=50343

m=vu=h2h1h2=503432532252h2=+5043

The x-coordinate of the images

=50vcos30+h2cos6025

The y-coordinate of the images

=vsin30+h2sin60253



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