question_answer

When a light ray enters a refracting medium, it is found that the magnitude of the angle of refraction is equal to half the angle of reflection. If n is the refractive index of the medium, then the angle of incidence is-

A) \[2\text{ si}{{\text{n}}^{-}}^{1}\left( n/2 \right)~\]      

B) \[2\text{ }co{{s}^{-}}^{1}\left( n/2 \right)\]

C) \[co{{s}^{-}}^{1}\left( n/2 \right)\]                   

D) \[si{{n}^{-}}^{1}\left( n/2 \right)\]

Correct Answer: B

Solution :

\[sin\text{ }i\,\,=\,\,n\text{ }sin\,\,\frac{i}{2}\] \[2\,\,\sin \,\frac{i}{2}\,\,\cos \frac{i}{2}\,=\,n\,\,\sin \,\frac{i}{2}\] \[\cos \,\frac{i}{2}\,\,=\,\,\frac{n}{2}\] \[i=2\,\,{{\cos }^{-1}}\,\left( \frac{n}{2} \right)\]