Question

The wavefront of a light beam is given by the equation $x+2y+3z=c$ , (where c is arbitrary constant) then what is the angle made by the direction of light with the y-axis?

• A. ${\cos }^{-2}\frac{2}{\sqrt{14}}$
• B. ${\cos }^{-1}\frac{2}{\sqrt{14}}$
• C. ${\cos }^{-3}\frac{2}{\sqrt{14}}$
• D. ${\cos }^{-4}\frac{2}{\sqrt{14}}$

Answer 1

Answer: (B)

${\cos }^{-1}\frac{2}{\sqrt{14}}$

The wave front equations must be of form $ax+by+cz=1$ where $a^2+b^2+c^2=1$

$($ $a,b,c$ are cosines of angles made with $x,yx,z$ axes respectively $)$

applying this to the given equation$:$

$1^2+2^2+3^2=c^2$

$c^2=14$

$c=\sqrt{14}$

${\cos }^{-1}\frac{2}{\sqrt{14}}$

angle made with $y-$ axis is ${\cos }^{-1}\frac{2}{\sqrt{14}}$

Hence,

option $\left(B\right)$ is correct answer.