Question

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

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

Answer 1

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

the wavefront 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,y,z axes respectively)
applying this to the given equation ,
$1^2+2^2+3^2=c^2$
$c^2=14$
$c=\sqrt{14}$
angle made with y-axis is $co{s}^{-1}\frac{2}{\sqrt{14}}$
option $C$ is correct.