Q.

A glass hemisphere of radius R and of material having refractive index 1.5 is silvered on its flat face as shown in Fig. A small object of height h is located at distance 2R from the surface of hemisphere as shown in the figure. The final image will form

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a

at a distance of R from silvered surface, on the right side

b

on the object itself

c

at hemisphere surface

d

at a distance of 2R from the silvered surface, on left side.

answer is B.

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Detailed Solution

Here, three optical phenomena take place-first refraction, then reflection, and finally refraction

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For 1st refraction,

1.5V12R=1.51R

V=

i.e., rays after refraction get parallel to the axis and strike the mirror normally, get retraced back and final image is formed at the same place where the object is and of same size. Image would be real.

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A glass hemisphere of radius R and of material having refractive index 1.5 is silvered on its flat face as shown in Fig. A small object of height h is located at distance 2R from the surface of hemisphere as shown in the figure. The final image will form