question_answer

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3). A light beam incident normally on the face AB is totally reflected to reach on the face BC if

A) \[\sin \theta \ge \frac{8}{9}\]       

B)        \[\frac{2}{3}<\sin \theta <\frac{8}{9}\]

C) \[\sin \theta \le \frac{2}{3}\]       

D)        None of these

Correct Answer: A

Solution :

[a] The phenomenon of total internal reflection takes place during reflection at P. \[\sin \theta =\frac{1}{\begin{matrix}    \omega   \\    g  \\ \end{matrix}\mu }\]                               ...(i) When \[\theta \] is the angle of incidence at P Now, \[\begin{matrix}    \omega   \\    g  \\ \end{matrix}\mu =\frac{\begin{matrix}    a  \\    g  \\ \end{matrix}h}{\begin{matrix}    \omega   \\    g  \\ \end{matrix}\mu }=\frac{1.5}{4/3}=1.125\] Putting in (i), \[\sin \theta =\frac{1}{1.125}=\frac{8}{9}\] \[\therefore \]  sin\[\theta \] should be greater than or equal to\[\frac{8}{9}\]