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## Homework Statement

In front of a long, straight, white wall a laser is hanged. Laser is parallel to the wall when we decide to rotate it with constant angular velocity for ##\pi ## so that the laser spot travels over the entire wall. The duration of the turn lasts just as long as it takes for the laser light to travel to the wall and back to the laser. The wall radiates the light equally in all directions.

An observer standing next to the laser watches the light on the wall using a high speed camera. When will he first notice a bright spot and from which direction? How fast does the spot on the wall move at ##\pi / 4## (angle next to the perpendicular line)?

## Homework Equations

## The Attempt at a Solution

Let's start by saying that the laser is distance ##a## from the wall. The rotation therefore lasts for ##t=\frac{2a}{c_0}##, where ##c_0## is of course the speed of light.

##\pi =\omega t=\omega \frac{2a}{c_0}## and from here ##\omega =\frac{\pi c_0}{2a}##.

So finally ##\varphi (t)=\frac{\pi c_0}{2a}t## for ##t\in [0, \frac{2a}{c_0}]##.

I assume, that every spot on the wall that laser hits while rotating, becomes a light source that radiates light in all directions. Now I THINK I am somehow supposed to use Lagrangian multiplier to find the extreme value of time that light needs to come back to the laser. But I am having some really big troubles to find out what ##u## and ##v## are in ##min(u+\lambda v)##.

Is this even the right idea? Could somebody please help?