Question

A ray of light emerging from the point source placed at $P(1,2)$ is reflected at a point $Q$ on the $\text{y-axis}$ and then passes through the point $(6,9)$. Then

• A. $Q\equiv (0,3)$
• B. image of $P$ in $y-$axis is $(-1,2)$
• C. equation of incident ray is $x+y=3$
• D. equation of reflected ray is $y=x+3$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $Q\equiv (0,3)$
B image of $P$ in $y-$axis is $(-1,2)$
C equation of incident ray is $x+y=3$
D equation of reflected ray is $y=x+3$

Let $P^{\prime }$ be the reflection of $P$ in $\text{y-axis}$

$\therefore P^{\prime }=(-1,2)$

So, the equation of the line $P^{\prime }{Q}^{\prime }$(reflected ray)

$y-2=\frac{9-2}{6+1}(x+1)$

$\Rightarrow y=x+3$

$\therefore \text{y-axis}$ intersection with the line at $Q$

$\therefore Q=(0,3)$
So, the equation of incident ray $PQ$ will be $x+y=3$