A) \[\left( \sqrt{2}+1 \right)/2\]
B) \[\sqrt{\frac{5}{2}}\]
C) \[\frac{3}{2}\]
D) \[\sqrt{\frac{3}{2}}\]
Correct Answer: D
Solution :
At point A by Snell? slaw \[\mu =\frac{\sin {{45}^{o}}}{\sin r}\Rightarrow \sin r=\frac{1}{\mu \sqrt{2}}\] ?(I At point B, for total internal reflection, \[\sin {{i}_{1}}=\frac{1}{\mu }\] From figure, \[{{i}_{1}}={{90}^{o}}-r\] \[\therefore \]\[(\sin {{90}^{o}}-r)=\frac{1}{\mu }\]\[\Rightarrow \cos r=\frac{1}{\mu }\] ?(ii ) \[=\sqrt{\frac{2{{\mu }^{2}}-1}{2{{\mu }^{2}}}}\] ...(ii) \[\frac{1}{\mu }=\sqrt{\frac{2{{\mu }^{2}}-1}{2{{\mu }^{2}}}}\] Squaring both sides and then solving, we get \[\mu =\sqrt{\frac{3}{2}}\] \[\sqrt{\frac{3}{2}}\]You need to login to perform this action.
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