Question

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

• 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 $\sqrt{3}y=x-\sqrt{3}$

Mirror or reflecting surface/ boundary is $y=0$ or $x-axis$.

Light Ray: $x+\sqrt{3}y=\sqrt{3}$ or,

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

Slope: $m=\frac{-1}{\sqrt{3}}$. Meets x axis at $A(\sqrt{3},0)$.

The reflected ray will have a slope$=-m=\frac{1}{\sqrt{3}}$. Reason is that the angle of inclination with x axis becomes 180 - the angle of incident ray.

Also it passes through point $A$.

So the equation is: $y-0=\frac{(x-\sqrt{3})}{\sqrt{3}}.$

Or, $\sqrt{3}y-x+\sqrt{3}=0$.

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