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A glass sphere (\mu=1.5) of radius 8 \mathrm{~cm} is placed in sunlight. Where is the image of the sun formed by the light passing through the sphere? When refraction by second surface of sphere

 

Option: 1

4 \mathrm{~cm}


Option: 2

6 \mathrm{~cm}


Option: 3

15 \mathrm{~cm}


Option: 4

50 \mathrm{~cm}


Answers (1)

best_answer

As the sun is very far away, the incident ray can be assumed as coming from infinity.

For refraction at first surface:



\mathrm{Using \frac{m_{1}}{u}+\frac{m_{2}}{v}=\frac{m_{2}-m_{1}}{R}}
\mathrm{\Rightarrow \frac{1}{\infty}+\frac{1.5}{v_{1}}=\frac{1.5-1}{+8}}
\mathrm{\Rightarrow v_{1}=24 \mathrm{~cm}}.

The rays try to converge at \mathrm{\mathrm{I}_{1}} and hence for the second surface it is a virtual object. For second surface:

\frac{\mathrm{m}_{1}}{\mathrm{u}}+\frac{\mathrm{m}_{2}}{\mathrm{v}}=\frac{\mathrm{m}_{2}-\mathrm{m}_{1}}{\mathrm{R}}
\mathrm{u}=-(24-16)=-8 \mathrm{~cm}
\Rightarrow \frac{1.5}{-8}+\frac{1}{v_{2}}=\frac{1-1.5}{-8}
\Rightarrow v_{2}=4 \mathrm{~cm}.

Hence the final image is formed at \mathrm{I}_{2} which is 4 \mathrm{~cm} from the other surface of the sphere.

Posted by

Rishabh

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