question_answer

Consider the figure shown. Reflected ray AB and refracted ray AC are perpendicular. Refractive index of the material of the sphere is-

A) \[\sqrt{1.5}\]                 

B) \[\sqrt{2}\]

C) \[\sqrt{3}\]                                

D) \[\sqrt{2.5}\]

Correct Answer: C

Solution :

\[r+90+60\text{ }=180{}^\circ \] \[\therefore \,\,\,r\,\,=\,\,30{}^\circ \] Snell law \[\mu \,sin\text{ }r=1\,\,\times \,\,sin\text{ }60{}^\circ \] \[\mu \,\,\times \,\,sin\text{ }30\,\,=\,\,1\,\,\times \,\,sin\text{ }60{}^\circ \] \[\frac{\mu }{2}\,\,=\,\,\frac{\sqrt{3}}{2}\] \[\mu =\sqrt{3}\]