A ray of light is incident along a line which meets another line $7x-y+ 1 = 0$, at the point $(0, 1)$. The ray is then reflected from this point along the line,$y + 2x = 1$. Then the equation of the line of incidence of the ray of light is

Let slope of incident ray be m. Now angle of incidence = angle. of reflection

$\begin{array}{l}\therefore \left|\frac{m-7}{1+7m}\right|=\left|\frac{-2-7}{1-14}\right|=\frac{9}{13}\end{array}$

$\Rightarrow \frac{m-7}{1+7m}=\frac{9}{13}$ or$\frac{m-7}{1+7m}=-\frac{9}{13}$

$\begin{array}{l} \\ \Rightarrow 13m-91=9+63m\text{ or }13m-91=-9-63m\\ \end{array}$

$\Rightarrow 13m - 91 = 9 + 63m$ or$13m-91=-9-63m$

$\Rightarrow 50m=-100$ or $76m=82\Rightarrow m=-2$ or $m=\frac{41}{38}$

$\therefore$ Equations of incident line at (0, 1) are

$y-1=-2(x-0)$ or $y-1=\frac{41}{38}(x-0)$

i.e., $2x+y-1=0$ or $38y-38-41x=0$