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)