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Q.

A parallel bean 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 approximation.

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a

The rays are focused at 12 cm from the point P to the right, in the situation 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 focussed at distance 18 cm from point P to the right. 
 

d

If the rays are incident at the curved surface (figure (ii)) then these are focussed at distance 14 cm from point P to the right.
 

answer is A, D.

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Detailed Solution

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1ϑ1.5=(11.5)(6)ϑ=+12cm 1.5ϑ1=(1.51)(+6)ϑ=+18cm   and   (186)1.5=h21h2=8cm

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