A) \[n>\sqrt{2}\]
B) \[n=1\]
C) \[n=1.1\]
D) \[n=1.3\]
Correct Answer: A
Solution :
From the following figure r + i = 900 Þ i = 900 ? r For ray not to emerge from curved surface i > C Þ sin i > sin C Þ sin (90o ? r) > sin C Þ cos r > sin C Þ \[\sqrt{1-{{\sin }^{2}}r}>\frac{1}{n}\] \[\left\{ \because \,\sin C=\frac{1}{n} \right\}\] Þ \[1-\frac{{{\sin }^{2}}\alpha }{{{n}^{2}}}>\frac{1}{{{n}^{2}}}\]Þ \[1>\frac{1}{{{n}^{2}}}(1+{{\sin }^{2}}\alpha )\] Þ \[{{n}^{2}}>1+{{\sin }^{2}}\alpha \] Þ \[n>\sqrt{2}\] {sin i ® 1} Þ Least value \[=\sqrt{2}\]You need to login to perform this action.
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