A) \[{{45}^{\circ }}\]
B) \[{{60}^{\circ }}\]
C) \[{{90}^{\circ }}\]
D) \[{{180}^{\circ }}\]
Correct Answer: A
Solution :
Key Idea: In the position of minimum deviation angle of incidence is equal to angle of emergence. Let a ray of monochromatic light \[PQ\] be incident on face \[AB\]. \[PQRS\] is path of light ray, Where \[i\] is angle of incidence, \[r\]angle of refraction, \[r\] angle of incidence and \[i'\] angle of emergence. In position of minimum deviation \[i'=i,\,\,r'=r,\,\delta ={{\delta }_{m}}\] \[\therefore \] \[2r=A\,\,or\,\,r=\frac{A}{2}\] Given, \[A={{60}^{\circ }}\], r\[r=\frac{60}{2}={{30}^{\circ }}\] Also from Snell?s law \[\mu =\frac{\sin \,i}{\sin \,r}=\frac{\sin \,i}{\sin \,{{30}^{\circ }}}\] \[\sqrt{2}=\frac{\sin \,i}{\sin \,{{30}^{\circ }}}\] \[\Rightarrow \] \[\sin \ i=\sqrt{2}\times \frac{1}{2}=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[i={{45}^{\circ }}\]You need to login to perform this action.
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