question_answer

ACB is right - angle prism with other angles as \[60{}^\circ \] and\[30{}^\circ \]. Refractive index of the prism is 1.5. AB has thin layer of liquid on it as shown. Light falls normally on the face AC. For total internal reflections, maximum refractive index of the liquid

A) 1.4       

B) 1.3

C) 1.2       

D) 1.6

Correct Answer: B

Solution :

[b] Clearly, \[{{i}_{c}}\le 60{}^\circ \] So, maximum possible value of \[{{i}_{c}}\]is \[60{}^\circ \]. Now, \[_{1}{{\mu }_{g}}=\frac{1}{\sin \,{{i}_{C}}}\] \[\frac{{{\mu }_{g}}}{{{\mu }_{i}}}=\frac{1}{{{\operatorname{sini}}_{c}}}\text{ or }{{\mu }_{1}}={{\mu }_{g}}{{\operatorname{sini}}_{c}}=1.5\sin 60{}^\circ =1.5\times \frac{\sqrt{3}}{2}\] \[=1.5\times 0.866=1.299=1.3\]