question_answer

Light is refracted \[\mu \]= 3/2 to water \[\mu \] = 4/3. For total internal reflection sin i will be equal to:

A) \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\]

B)        \[{{45}^{0}}\]                    

C)        \[{{60}^{0}}\]                    

D)        \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]

Correct Answer: D

Solution :

We know that for total internal reflection, the incident angle must be greater than or equal to the critical angle for which the refracted angle is \[\text{9}{{\text{0}}^{\text{o}}}\] Here,                     \[\frac{{{\mu }_{2}}}{{{\mu }_{1}}}=\frac{\sin i}{\sin {{90}^{o}}}\] \[\frac{4/3}{3/2}=\sin i\]or \[i={{\sin }^{-1}}\left( \frac{8}{9} \right)\]