Light wave interference questions

[rp1220]

I have two questions concerning what happens when light interference occurs.

In destructive interference of coherent light beams, how is energy conserved, both when interference occurs in air and in a vacuum.

When non coherent light beams intersect is space there is no interference pattern seen. This is apparently due to the random distribution of the phases of the beams. But does this mean there is no interference or just no pattern to the interference which occurs which is then invisible.

 

[grzz]

When non coherent light beams intersect is space there is no interference pattern seen. This is apparently due to the random distribution of the phases of the beams.

The beams do interfere and there is a pattern. But this pattern changes so fast that the human eye cannot follow it.

 

[chrisbaird]

This has been discussed at length in other threads, but I will give you a summary. If destructive interference occurs in a medium, some of the energy may be lost to the medium. If destructive interference occurs in vacuum, the energy is displaced to where there is no destructive interference. For instance, in thin film interference, an incident beam reflects off the front as well as back surface of the film (think soap bubble). If the wavelength and the film thickness are set right, then the two reflected beams will destructively interfere in the vacuum above the film. The energy is not destroyed, rather all of the incident energy is transmitted through the film to the other side. In fact, you could argue that the two reflected waves that cancel are mathematical entities and there is actually no physical wave that gets reflected because it is forbidden to do so.

The concept is similar to optical modes in a waveguide. A certain waveguide only supports certain optical modes to propagate. The other modes experience destructive interference and are thus forbidden. If you shine light at the mouth of a waveguide at a non-supported frequency/mode (one at which destructive interference occurs), it will not enter and be destroyed physically, even though we describe mathematically its non-propagation by the destructive interference of multiply-reflected waves. Rather, the light will simply be reflected (scatter) off the mouth of the waveguide.

In another example, bound electrons in atoms only take on certain quantum orbital shapes. Other shapes you could dream up are not allowed because of destructive interference of the wave with itself if the shape is not right. This does not mean that energy is constantly being destroyed in atoms because of destructive interference, rather that the energy is forbidden from ever entering those non-physical states.

 

[McLaren Rulez]

Regarding your first question, I think that the energy is redistributed to the parts where constructive interference is taking place. So for instance, in a double slit experiment, the energy in the places where constructive interference is taking place is more than the sum of the individual energies from the waves.

EDIT: Looks like chrisbaird posted a much more comprehensive answer.