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← JEE Advanced 2016 · Paper 2
PhysicsSingle correct+3 / -1Question 5 of 54

JEE Advanced 2016 · Paper 2, Physics question 5

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°\theta=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)(x,y) at which the image is formed are

Optical bench along the x-axis: an object arrow at (−50, 0); a convex lens (f = 30 cm) at the origin (0, 0); 50 cm to the right, a convex mirror whose axis (dashed) is tilted at θ = 30° to the x-axis, sloping down to the right towards its centre of curvature at (50 + 50√3, −50), with R = 100 cm marked along the axis.
Choose one option
Answer and worked solution

Official answer: C

Lens. u=−50u=-50 cm and f=30f=30 cm give v=75v=75 cm. This image lies 25 cm behind the mirror's pole at (50, 0), so it is a virtual object for the mirror.

Mirror (the intended paraxial treatment). The convex mirror has f=R/2=50f=R/2=50 cm. With the object 25 cm behind it:
1v+125=150  ⟹  v=−50 cm.\frac1v+\frac1{25}=\frac1{50}\implies v=-50\text{ cm}.
The image is real, 50 cm in front of the mirror.

Tilt. Tilting the mirror by θ=30°\theta=30° turns the reflected beam, and the image, through 2θ=60°2\theta=60° about the pole. The image lies 50 cm from (50, 0), along a direction 60° above the −x-x axis:
(x,y)=(50−50cos⁡60°, 50sin⁡60°)=(25, 253).(x,y)=(50-50\cos60°,\ 50\sin60°)=(25,\ 25\sqrt3).

(C)

Topics:Combination of lenses and mirrorsSpherical mirrorsThin lenses and lens maker's formula
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