Question

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$-axis. Equation of the reflected rays is

• A. $\sqrt{3}y=x-\sqrt{3}$
• B. $y=\sqrt{3}x-\sqrt{3}$
• C. $\sqrt{3}y=x-1$
• D. $y=x+\sqrt{3}$

Answer 1

Answer: (A)

$\sqrt{3}y=x-\sqrt{3}$

$x+\sqrt{3}y=\sqrt{3}$
$y=\frac{-1}{\sqrt{3}}x+1$
Hence the line makes an angle of $-{30}^0$ with respect to x axis.
Hence the reflected line will make a $+{30}^0$ angle with the x axis.
Thus the equation of the line will be of the form
$y=\frac{x}{\sqrt{3}}+c$ ...(i) where c is a constant.
Now the reflected line and the original line meet where the original line cuts the x axis.
The point is $x=\sqrt{3}$
Hence substituting the point $(\sqrt{3},0)$ in equation i gives us
$0=1+c$
Or
$c=-1$
Hence the equation of the reflected line will be
$y=\frac{x}{\sqrt{3}}-1$
$\sqrt{3}y-x+\sqrt{3}=0$