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

Question

Aicharya · Accepted Answer

Let the slope of incident ray be $\mathrm{m}$ $\therefore$ Angle of incidence $=$ angle of reflection $\Rightarrow\left|\frac{m-7}{1-7 m}\right|=\left|\frac{-2-7}{1-14}\right|=\frac{9}{13}$ $\Rightarrow \frac{m-7}{1-7 m}= \pm \frac{9}{13}$ $\begin{aligned} & \Rightarrow 13 m-91=9+63 m \text { or } 13 m-91=-9-63 m \\ & \Rightarrow 50 m=-100 \text { or } 76 m=82 \\ & \Rightarrow m=-\frac{1}{2} \text { or } m=\frac{41}{38}\end{aligned}$ When $m=\frac{41}{38}$ The required equation of line is: $y-1=\frac{41}{38}(x-0) \Rightarrow 41 x-25 y+25=0$

A ray of light incident along a line, meets another line $7 x-y+1=0$ at the point $(0,1)$ and it is then…

Solution