Optics Question 460
Question: The wave front of a light beam is given by the equation $ x+2y+3x=c $ (where c is arbitrary constant), then the angle made by the direction of light with the y-axis is
Options:
A) $ {{\cos }^{-1}}\frac{1}{\sqrt{14}} $
B) $ {{\sin }^{-1}}\frac{2}{\sqrt{14}} $
C) $ {{\cos }^{-1}}\frac{2}{\sqrt{14}} $
D) $ {{\sin }^{-1}}\frac{3}{\sqrt{14}} $
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Answer:
Correct Answer: C
Solution:
[c] Here, direction of light is given by normal vector $ \vec{n}=\hat{i}+2\hat{j}+3\hat{k} $
$ \therefore $ Angle made by the $ \vec{n} $ with y-axis is given by $ \cos \beta =\frac{2}{\sqrt{1^{2}+2^{2}+3^{2}}}=\frac{2}{\sqrt{14}} $
