question_answer

Two right angled prisms having the same refracting angle \[60{}^\circ \] are placed as shown in the figure. A ray of light incident on the first prism is finally deviated by an angle \[90{}^\circ \]. The refractive index of second prism is \[\sqrt{2}\]. The refractive index of the first prism is equal to

A) \[\sqrt{2}\frac{\sin 30{}^\circ }{\sin 60{}^\circ }\]

B) \[\sqrt{2}\frac{\sin 45{}^\circ }{\sin 60{}^\circ }\]

C) \[\sqrt{2}\frac{\sin 15{}^\circ }{\sin 60{}^\circ }\]                     

D) \[\sqrt{2}\frac{\sin 60{}^\circ }{\sin 30{}^\circ }\]

Correct Answer: B

Solution :

[c]  Snell's law at C \[1\times \sin 90{}^\circ =\sqrt{2}\,\sin {{r}_{2}}\] \[{{r}_{2}}=45{}^\circ \] Snell's law at B   \[\sqrt{2}\sin 15{}^\circ =1\sin r\]        ...(i) Snell's law at A  \[\mu .\sin 60{}^\circ =1.\sin r\]      ...(ii) From (i) and (ii), \[\mu .\sin 60{}^\circ =\sqrt{2}\sin 15{}^\circ \] \[\mu =\sqrt{2}\frac{\sin 15{}^\circ }{\sin 60{}^\circ }\]