Question

The wavefront 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

• A. $co{s}^{-1}\frac{1}{\sqrt{4}}$
• B. $si{n}^{-1}\frac{2}{\sqrt{14}}$
• C. $co{s}^{-1}\frac{2}{\sqrt{14}}$
• D. $si{n}^{-1}\frac{3}{\sqrt{14}}$

Answer 1

The correct option is C $co{s}^{-1}\frac{2}{\sqrt{14}}$

Here, direction of light is given by normal vector

$\overrightarrow{n}=\hat{i}+2\hat{j}+3\hat{k}$

$\therefore$ Angle made by the $\overrightarrow{n}=\hat{i}+2\hat{j}+3\hat{k}$ with the y axis is given by :-

cos $\beta$= $\frac{\overrightarrow{n}}{|\overrightarrow{n}|}$ = $\frac{2}{\sqrt{1^2+2^2+3^2}}$ = $\frac{2}{14}$

$\beta$ = $co{s}^{-1}\left(\frac{2}{\sqrt{14}}\right)$