- #1

Almeisan

- 334

- 47

I think at this point we are working with classical waves, moving towards QM eventually.

The idealization we work with is this. We have a light source creating a wave [itex] ψ(x,t)=Acos(ωt+kx)[/itex] .

The light beam hits a beam splitter/partially reflective mirror. Half the intensity is reflected, half the intensity is transmitted. Say we do this 3 times to get 4 beams.

As [itex]I = A^2[/itex] , so the amplitude of these waves is A/2 and we get four waves of [tex] ψ(x,t)=\frac{A}{2}cos(ωt+kx+Φ) [/tex]

Now, for combining waves, one is supposed to be able to add them. If the Φ term is made exactly the same, they should be completely identical. One should get [tex] ψ(x,t)=4(\frac{A}{2}cos(ωt+kx+Φ)) [/tex] .

So now we have 2 times the original intensity. This is asymmetrical and something must be wrong somewhere. I don't know if this mixes different idealizations, say QM light as a photon phenomena and classical EM waves phenomena.

Is it somehow impossible to get 100% constructive interference after adding these waves? I know QM light isn't described by a simple sinusoidal wave. I always thought the issue of getting 4 times the intensity with interference is that you get 0 intensity at other spots, so energy is conserved. But there are no plane waves or spherical waves here.

The solution to some problems given clearly show that it adds two beams of 1/4th intensity to get a beam with equal intensity and amplitude to the original beam.

Shouldn't waves be recombined the same was as they are split? So either half the intensity and double the intensity, OR, half the amplitude and double the amplitude.