Divergence post reflection

[VW]

Divergence explains the ammount the beam will expand each meter, over a given distance. But what I was wondering was, how the divergence is effected after a reflection and whether using a device to reduce divergence (i.e beam expander) will increase brightness after a reflection.

In a few weeks I'll have the beam expander for the Spartan, so I was interested in finding out. Theoretically, the beam expander will make the beam brighter over a longer distance (not taking into account power loss after installation) than usual. Would reducing the divergence to .12mrad have any increasing effect off of reflections?

 

[likewhat]

assuming it reflects of a flat surface the divergence will remain unchanged

 

[FrothyChimp]

Grab a physics book and head to the optics section. You will find some laws about the angle of incidence on a reflector. Theta sub1 = theta sub2 is usually how it is explained. Of course if you are using a regular silver backed mirror you will get a front reflection, refraction through the glass and a second reflection off the silvering so you end up with two beams, one brighter than the other.

 

[Foobario]

But what I was wondering was, how the divergence is effected after a reflection

The reflective surface basically 'folds' the light. If you draw the expanding/contracting beam as a triangle of light, and draw a mirror crossing its path, it will reflect (and continue to expand or contract just as it was prior to the reflection) in the direction you get if you fold the paper at the mirror line. If the mirrors are flat and front-surface, you can do this numerous times and it won't distort the beam. It takes something non-linear, like a lens or a curved mirror, to cause such a beam to break away from its triangle fanout and converge/diverge the way you want it to.

 

[Foobario]

Re: some pills make you larger

Another mental image:

Shine your laser into a big mirror (at an angle, so the reflection doesn't hit you or anyone else) and the image of the beam in the mirror is exactly the same as if the mirror were merely a window looking into another room. The laser line appears to be straight, hitting the far wall of that 'other' room right where it would hit your far wall if your room was twice as big.

Since the beam is a straight line 'passing through' the plane of the mirror, we know that the angle the beam makes with the mirror is the same on both sides of the mirror. Which, thinking of the mirror as a mirror now, means that the angle reflected back into our world must be the same too... this gives us the familiar "angle of incidence equals angle of reflection" idea.

So now, to collimate my diverging explanation: think of a diverging ray as 2 lines: one on the left side of the beam, another on the right. Each of those lines will behave exactly the same as the single beam did above, which means a diverging beam will continue to be a diverging beam in the room beyond the mirror. That means that their reflection back into our world must behave the same way on our side of the mirror. So the reflection of the beam, whether diverging or not, will hit the wall behind you exactly the same way as it would hit the wall of the room beyond the mirror, or your far wall if your room was twice as big.

You might notice I never mentioned the fact that mirrors seem to reverse left and right. If you set two lasers side by side and parallel, with the green one on your left, the spot on the wall in the mirror world will be green on the left side. But if you then turn around (leaving the lasers the way they were), you'll see that the reflected spot on the wall opposite the mirror has the green on your right. But think of that whole scene as seen from above: you'll see that the lasers, the points where the lasers hit the mirror, the spots on the wall in the mirror world, and the reflected spots on the wall opposite the mirror all have the green on the same side. If you think about it, this explains why mirrors reverse left and right but don't reverse up and down.

 

[Foobario]

Also: if a converging laser comes to a point and then passes that point, everything is reversed from that point on... but it still behaves the way I wrote above. (Just thought I'd make this note because if you actually try the green-red experiment and you 'cross the beams' everything turns out backwards from that point on.) This is easy to see with a magnifying glass - hold it up close to something, and the image looks correct... but pull the lens back farther and the image appears reversed (both left-to-right and up-to-down) once you pass the focal length.