Question

A ray of light along x+√3y=√3 gets reflected upon reaching x-axis. Find the equation of reflected ray.

Answer 1

let the slope reflected line be m and of main ray be M

slope of this line is
M = -A/B = -1/√3

also, a light reflects at an angle 90°
so, Mm = -1
(-1/√3)m = -1
m = √3

now,
at x axis
y = 0
so, x+√3y = √3
x+√3(0) = √3
x = √3

so, equation of required line
√3(x-√3) = y-0
√3x-3 = y
√3x-y = 3

Answer 2

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 = -1/sqrt(3). Meets x axis at A(sqrt(3), 0).

The reflected ray will have a slope = - m = 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 = (x - sqrt(3)) /sqrt(3).
Or, sqrt(3) y - x + sqrt(3) = 0.