Question

A ray of light is sent along the line x − 2y + 5 = 0. Upon reaching the line 3x − 2y + 7 = 0, the ray is reflected from it. Find the equation of the reflected ray.

Answer 1

See Fig.  We have

x - 2y + 5 = 0 (Incident ray ..(1)

 3x - 2y + 7 = 0 (Surface line) ....(2)

P = (−1, 2) is the point of incidence of the lines given in Eqs. (1) and (2). Hence, the equation of the normal at P(−1, 2) is

y - 2 = -2/3(x + 1)

2x + 3y - 4 = 0   ....(3)

 Let m be the slope of the reflected ray. Since the normal at P makes equal angles with the incident line and reflected line, we have

 However, m ≠ 1/2 . (\(\because \) Slope of incident ray is 1/2 and reflected ray never be parallel to incident ray)

So that the reflected line is 

y - 2 = 29/2(x +1)