Destructive interference at a surface

[God Plays Dice]

Take two lasers of the same intensity and wavelength and aim them at 30 degrees at the same spot on a mirror, so that at the surface the waves cancel perfectly.

What happens? How can the wave be reflected if there is no field present?

 

[Dale]

Take two lasers of the same intensity and wavelength and aim them at 30 degrees at the same spot on a mirror, so that at the surface the waves cancel perfectly.

This is not possible.

 

[God Plays Dice]

Why not?

 

[God Plays Dice]

Is just like when two waves cross over each other and cancel

 

[sophiecentaur]

Is just like when two waves cross over each other and cancel

This will only happen in a small region. On either side of the cancellation region, the phases will not be 180° out and you will not get cancellation. Further still and the phase difference will be 0°, giving a peak. The total energy must remain unchanged - it's just rearranged into 'fringes' of maxes and mins. With an angle of 30° between the beams, the fringes will be quite close together.
This all assumes that the two lasers are perfectly synchronised - which is hard to achieve.
Is that a satisfactory answer?

 

[God Plays Dice]

I don't see where there will be constructive interference. At the mirror surface I certainly can't see it, apart from the magnetic fields as they are at an angle to each other and as you make the angle closer to 0 they cancel. however along the beam I can see the electric fields canceled and the magnetic fields added everywhere.

It seems the wave forms a magnetic wave that doesn't move and has a node at the mirror

 

[God Plays Dice]

Sry it is a magnetic standing wave (it does move) but has a node at the mirror

 

[God Plays Dice]

It's a standing wave, with electric and magnetic field 90 degrees out. When two waves are directed at each other that's what occurs

 

[Dale]

Why not?

If they cancel in one spot they will not cancel in the spot nearby. This is easiest to work out using plane waves, but the same conclusion will hold for any valid field.

 

[Dale]

I can see the electric fields canceled and the magnetic fields added everywhere.

It seems the wave forms a magnetic wave that doesn't move and has a node at the mirror

Yes, this also happens when two waves cross at an angle.

 

[nasu]

Is this 30 degrees the angle between the beams? Or you mean that they are both aimed at 30 degrees incidence angle?

 

[Dale]

Is this 30 degrees the angle between the beams? Or you mean that they are both aimed at 30 degrees incidence angle?

That is a good question. I had assumed each was 30 degrees incidence from opposite sides of the normal. But now I am not sure of the intended geometry.

 

[sophiecentaur]

Is this 30 degrees the angle between the beams? Or you mean that they are both aimed at 30 degrees incidence angle?

I was assuming that there is 30 degrees between them. It would not be possible to arrange for them to be incident from exactly the same direction in such a say that they would cancel out completely because the sources would have to be coincident / superposed on one another. Then there could be no output.

 

[nasu]

I know that you know that is not possible. However the question with two beams "overlapping everywhere" was asked (and discussed) several times already on the forum, I believe.
So it is not obvious that it should be dismissed and answer a different question just because it makes more sense.:)