Question

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 :

• A. $41x–25y+25=0$
• B. $41x-38y+38=0$
• C. $41x+38y–38=0$
• D. $41x+25y–25=0$

Answer 1

The correct option is B $41x-38y+38=0$

From the question we can draw the following figure

Now,from laws of reflection, we know that
angle between normal and incident ray=angle between normal and reflected ray.
Let slope of incident ray be $m$,
slope of normal=$-\frac{1}{7}$ and slope of reflected ray=$-2$
$\Rightarrow \frac{m+\frac{1}{7}}{1-\frac{m}{7}}=\frac{-\frac{1}{7}+2}{1+\frac{2}{7}}\Rightarrow m=\frac{41}{38}$
So, the equation of incident ray
$y-1=\frac{41}{38}(x-0)\Rightarrow 41x–38y+38=0$