question_answer

A ray of light is incident at an angle \[i\]on a glass slab of refractive index \[\,\mu .\]The angle between reflected and refracted light is \[{{90}^{o}}.\] Then, the relationship between \[i\]and \[\,\mu .\]is

A)  \[i={{\tan }^{-1}}\left( \frac{1}{\mu } \right)\]

B)  \[\tan \,i=\mu \]

C)  \[\sin \,i=\mu \]

D)  \[\cos \,i=\mu \]

Correct Answer: B

Solution :

 As situation can be diagrammatically as below From law of reflection \[i=\theta \] Now, \[\theta +r+{{90}^{o}}={{180}^{o}}\] \[\Rightarrow \] \[i+r+{{90}^{o}}={{180}^{o}}\] \[r={{90}^{o}}-i\] Also, from Snells law \[\frac{\sin i}{\sin r}=\mu \Rightarrow \frac{\sin i}{\sin ({{90}^{o}}-i)}=\frac{\sin i}{\cos i}=\mu \] \[\Rightarrow \] \[\tan \,i=\mu \]