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Question

In the figure shown, a point object O is placed in air on the principal axis. The radius of curvature of the spherical surface is 60 cm. I is the final image formed after all refractions and reflections.

A
If x=120 cm, then I is formed on O for any value of y
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B
If x=120 cm, then I is formed on O only if y=120 cm
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C
If x=120 cm, then I is formed on O only if y=110 cm
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D
If x=120 cm, then I is formed on O only if y=360 cm
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Solution

The correct option is A If x=120 cm, then I is formed on O for any value of y
Given,
refractive index of air, μa=1,

refractive index of spherical surface material, μg=32,

For the first refraction: On using mirror formula,

μgvμau=μgμaR

Taking case of option (a):

3/2v1(120)=3/21+60

32v=0

v=

Thus, rays become parallel to principal axis after refraction. It will fall normally on the plane mirror and will retrace the path.

Hence, final image will form at the object O itself and it does not depend on value of y.

Therefore, option (a) is correct.
Why this question ?Tip: When a ray falls normally on amirror, it retraces its path.


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