question_answer

A beam of parallel light rays is incident on a solid transparent sphere of refractive index \[\mu \]. If a point image is produced just at the back of the sphere, what is the refractive index of the sphere?

A)  2.0                        

B)  2.3    

C)  2.5                        

D)  2.7

Correct Answer: A

Solution :

                 Let C be the centre and \[{{P}_{1}}\] and \[{{P}_{2}}\] the poles of the sphere. A ray OA parallel to a diameter is first refracted into the glass along AB. For refraction at A from air to glass, we have                 \[\frac{\mu }{v}-\frac{1}{u}-\frac{\mu -1}{R}\] Here u \[=\infty \] and \[v=2R\] \[\therefore \]  \[\frac{\mu }{2R}-\frac{1}{\infty }=\frac{\mu -1}{R}\]                                 \[\frac{\mu }{2R}=\frac{\mu -1}{R}\]                                 \[\mu =2\mu -2\]                                 \[\mu =2\]