A parallel beam of light is incident normally on the flat surface of a hemisphere of radius `6 cm` and refractive index `1.5`, placed in air as shown in figure (i). Assume paraxial ray approxiamtion.
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Options

A. The rays are focused at `12 cm` from the point `P` to the right, in the solutation as shown in figure (i)
B. The rays are focused at `16 cm` from the point `P` to the right, in the situation as shown in figure (i).
C. If the rays are incident at the curved surface (figure (ii)) then these are focused at distance `18 cm` from point `P` to the right
D. If the ray are incident at the curved surface (figure(ii)) then these are focused at distance `14 cm` from point `P` to the right.

Answer

A, D

Explanation

As in figure (i), rays are parallel incident on curved part
Therefore `(1)/(v)-(3//2)/(infty)=(1-3//2)/(-6)`
`rArr v=12 cm`
For figure (ii), image created by curved part acts as object for the flat part.
For curved part
`(1.5)/(v)-(1)/(infty)=(0.5)/(6) rArr v=18 cm`
from falt surface, object is at `12 cm` to the right.
for flat part
`(1)/(v)-(1)/(8)=0 rArr (1)/(v)-(1)/(8) rArr v=8`
So distance of final image from `P=6 +8 = 14 cm`. (right)