A) \[2x-3y+3=0\]
B) \[3x-2y+3=0\]
C) \[21x-7y+1=0\]
D) \[21x+7y-1=0\]
Correct Answer: B
Solution :
The point of intersecton of \[{{x}_{1}},\,{{x}_{2}},\,{{x}_{3}}\] and \[{{k}_{1}},\,{{k}_{2}},\,{{k}_{3}},\,{{k}_{4}}....,\] is \[{{x}_{5}}={{x}_{1}}+{{x}_{2}}+{{x}_{3}}+...\] \[\Rightarrow \] Point \[\frac{mg}{{{k}_{s}}}=mg\,\left( \frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}+\frac{1}{{{k}_{3}}}+... \right)\] is the point of incidence. \[\therefore \] Slope of incident ray \[\frac{1}{{{k}_{s}}}-\frac{1}{{{k}_{1}}}+\frac{1}{{{k}_{2}}}+\frac{1}{{{k}_{3}}}+...\] and Slope of normal = 1 Let slope of refracted ray be m. Then, \[{{k}_{1}}=k,\] \[{{k}_{2}}=2k,\] \[{{k}_{3}}=3k,...\] \[\frac{1}{{{k}_{s}}}=\frac{1}{k}+\frac{1}{2k}+\frac{1}{4k}+\frac{1}{8k}+...\] The equation of the striaght line containing the refracted ray is \[\Rightarrow \] \[\frac{1}{{{k}_{s}}}=\frac{1}{k}\,\left( 1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+... \right)\] \[\Rightarrow \]
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