A) \[9{{x}^{2}}-12xy\cos 6+4{{y}^{2}}\]
B) \[-36{{\sin }^{2}}\theta \]
C) \[36{{\sin }^{2}}\theta \]
D) \[36{{\cos }^{2}}\theta \]
Correct Answer: A
Solution :
Rays comes out only from CD, means rays after refraction from AB get totally internally reflected at AD. From the figure, \[3y-2+6=0\] \[y+3z+6=0\] \[3y-2z+6=0\]and \[a=2\hat{i}=2\hat{j}-2\hat{k}\] (for total internal reflection at AD) where, \[b=\hat{i}+\hat{j}\]or\[a.c=\left| c \right|,\left| c-a \right|=2\sqrt{2}\] \[a\times b\]\[\left| (a\times b)\times c \right|\] Now, applying Snell's law at face AB, we wet \[\frac{2}{3}\] \[\frac{3}{2}\] \[\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\left\{ y+{{\left( \frac{dy}{dx} \right)}^{2}} \right\}}^{1/4}}\]\[1+\frac{2}{3}+\frac{6}{{{3}^{2}}}+\frac{10}{{{3}^{3}}}+\frac{14}{{{3}^{4}}}+...\] \[\frac{x}{2}-\frac{y}{3}=1\]You need to login to perform this action.
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