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. ${\sin }^{-1}\left(\frac{2}{\sqrt{14}}\right)$
• B. ${\cos }^{-1}\left(\frac{2}{\sqrt{14}}\right)$
• C. ${\sin }^{-1}\left(\frac{3}{\sqrt{14}}\right)$
• D. ${\cos }^{-1}\left(\frac{1}{\sqrt{14}}\right)$

Answer 1

The correct option is B ${\cos }^{-1}\left(\frac{2}{\sqrt{14}}\right)$

Here, direction of light of equation $x+2y+3x=c$, is given by normal vector,

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

Angle made by the $\hat{n}$ with $y-$axis is given by,

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

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

Hence, $\left(B\right)$ is the correct answer.