Question

A ray of light travelling along the line 2x − 3y + 5 = 0 after striking a plane mirror lying along the line x + y = 2 gets reflected. Find the equation of the straight line containing the reflected ray.

Answer 1

The point of intersection of the lines 2x − 3y + 5 = 0 and x + y = 2 is (1/5,9/5) which is also the point of incidence. Slope m of the normal to the mirror (i.e. normal to the line x + y = 2) is 1. Now, the incident ray and reflected ray both are equally inclined to the normal and are on opposite side of it. The slope of incident ray is

m₁ = 2/3

Let the slope of the reflected ray be m₂. Then

Therefore, the equation of the straight line that contains the reflected ray is