A moveable screen slides along a mirrored corridor towards a
centrally placed light source. A ray of light from that source is
directed towards a wall of the corridor, which it strikes at
$45^\circ $ before being reflected across to the opposite wall and
so on until it hits the screen.
If the screen is $20$ metres down the corridor from the light
source and if the corridor is $2$ metres wide, find the position on
the screen where the point of light appears.
Now remember that
the screen is moveable. The distance, $d$, of the screen down the
corridor can change, so the position where the point of light
appears on the screen will depend on $d$. Can you find a function,
expressing the position of the light on the screen in terms of $d$?
If the ray
leaves the source making an angle $\theta$ with the direction of
the corridor, and the distance, $d$, of the screen down the
corridor can still change, the position where the point of light
appears on the screen will depend on $d$ and on $\theta$ . Can you
find this function?