A spotlight is positioned 20 meters from a wall. If the spotlight is to light a walkway on the other side of the wall, at what point should it be aimed to maximize the area illuminated?
Guide On Rating System
Vote
To maximize the area illuminated, the spotlight should be aimed at the midpoint of the walkway.
Here's why:
The spotlight is positioned 20 meters from the wall, so the radius of the light circle can be defined as r = 20 meters.
Let's assume that the walkway is a straight line parallel to the wall and perpendicular to the line connecting the spotlight to the wall. The spotlight should be aimed at the midpoint of this line.
If we aim the spotlight lower than the midpoint, the light beam will hit the ground before reaching the far end of the walkway. Similarly, if we aim the spotlight higher than the midpoint, the light beam will hit the wall before reaching the far end of the walkway. In both cases, the illuminated area will be smaller than if the spotlight were aimed at the midpoint.
Thus, to maximize the area illuminated, the spotlight should be aimed at the midpoint of the walkway.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99