Question

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

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

Answer 1

Answer: (B)

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

Equation of ray of light is $x+\sqrt{3}y=\sqrt{3}\Rightarrow y=\frac{-x}{\sqrt{3}}+1$

ray of light meets the $x-axis$ at $x=\sqrt{3}y=0$

slope of the line is $m=\frac{-1}{\sqrt{3}}\tan \theta =\frac{-1}{\sqrt{3}}\theta ={150}^0$

this line makes $-{30}^0$ with negative $x-axis$

so reflected ray will make ${30}^0$ with positive $x-axis$

so slope will be $m=\tan {30}^{0}m=\frac{1}{\sqrt{3}}$

equation of reflected ray is $y-0=\frac{1}{\sqrt{3}}(x-\sqrt{3})y=\frac{x}{\sqrt{3}}-1$

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

so option B is correct