A) equal to \[30{}^\circ \]
B) less than \[30{}^\circ \]
C) more than \[30{}^\circ \]
D) equal to \[60{}^\circ \]
Correct Answer: B
Solution :
Here, \[A={{r}_{1}}+{{r}_{2}}\] The critical angle C is given by- \[\sin \,C\,\,=\,\,\frac{1}{\mu }\,\,=\,\,\frac{1}{1.5}\,\,or\,\,C=42{}^\circ \,\,\] There will be no emergent ray when \[{{r}_{2}}>42{}^\circ \text{ }or\,\,A-{{r}_{1}}>42{}^\circ \] \[or\text{ }60-{{r}_{1}}>42,\text{ i}\text{.}e..,\text{ }{{r}_{1}}<18{}^\circ \] Now, \[\mu =\frac{\sin \,\,{{i}_{1}}}{\sin \,\,{{r}_{1}}}\] \[\therefore \text{ }sin\text{ }{{i}_{1}}=\,\,\mu \,sin\text{ }{{r}_{1}}\] If \[{{r}_{1}}\,\,<\,\,18{}^\circ ,\text{ }sin\,{{i}_{1}}<\mu \,\,sin\,\,18{}^\circ \] or \[{{i}_{1}}\,<\,\,{{\sin }^{-1}}\,(\mu \,\,sin\,\,18{}^\circ )\] or \[{{i}_{1}}\,<\,\,27{}^\circ \,\,(approx.)\]
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