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}} $



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