Question

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$ -axis, the equation of the reflected ray

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

Answer 1

The correct option is B $\sqrt{3}y=x-\sqrt{3}$

We have,

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

$y=\frac{-1}{\sqrt{3}}x+1$

On comparing $y=mx+c$, we get

$m=\tan \left(x\right)=-\frac{1}{\sqrt{3}}$

$\tan x=\frac{-1}{\sqrt{3}}$

Point $(\sqrt{3},0),m=\frac{1}{\sqrt{3}}$

Therefore,

$y=mx+c$

$0=\frac{1}{\sqrt{3}}\times \sqrt{3}+c$

$c=-1$

Therefore,

$y=\frac{1}{\sqrt{3}}x-1$

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

Hence, this is the answer.