A light ray travelling along the line y = 1, is reflected by a mirror placed along the line x = 2y. The reflected ray travels along which line?
My attempt: The line x=2y has slope 1/2 so the normal to the line will have slope -2. But what to do next?
$1)$ The lines will meet at the point $(2,1)$. Let's call $k$ then slope of the line $x=2y (line - t)$ .
$2)$ The incident angle is equal to the reflected angle. So the angle between the incident line and $t$ is the same as the one between $t$ and the reflected line.
$3)$ The angle between the incident line and $t$ is equal to the slope of the line $t$ because $y=1$ is parallel to the axis $x$, then the reflected line will have $\tan{(2k)}$ as its slope and it goes through the point $(2,1)$.
So,
$$\tan(2k)=\frac{2\tan k}{1-\tan ^2 k}= \frac{2.1/2}{1-(1/2)^2}=\frac{4}{3}$$
And then the line is
$$y=4x/3-5/3$$