Can 2 light sources of different wavelenghts interfere one in another?

[jaumzaum]

I'm asking because I was solving a double slit experiment problem in which the light was bichromatic (composed by 2 different colors, λ1 and λ2). What would we seen at the screen? Are there places where only one wavelength is observed? Can the 2 wavelenghts interfere to create a third wavelength?

Thank you
John

 

[DrDu]

Yes, the electric and magnetic fields just add up vectorially. The main practical problem in the detection is probably to maintain phase coherence between the two fields.
The creation of light with a different wavelength is possible at high field intensities ins so-called non-linear optical processes.
E.g. the light of green laser diodes is often generated by frequency doubling of light in the near IR.

 

[Lino]

... I was solving a double slit experiment problem ...

Why is this a double-slit experiment (why would it be different to two light sources shining on a screen)?

Regards,

Noel.

 

[Nugatory]

Why is this a double-slit experiment (why would it be different to two light sources shining on a screen)?

The slit, if narrow enough, simplifies the problem by making it so that there is only one straight-line path between the source of the light and the screen. That allows you to treat each slit as a point source of light.

 

[sophiecentaur]

Why is this a double-slit experiment (why would it be different to two light sources shining on a screen)?

Regards,

Noel.

If you shine light with two widely spaced spectral lines through the two slits then you will get two interference patterns, superimposed. They will tend to blur each other and mutually spoil visibility.

Similarly, of you use broad spectrum light (white light, say) only the first dark stripe will be detectable but the pattern soon degenerates into blurry coloured fringes. But this, again, is just the superposition of a continuum of individual interference fringes of different wavelengths.

A spatial interference pattern is only possible in a linear system when you can ensure that the signals received from two or more points in space have a constant phase relationship between them - so that you consistently get additive and subtractive interference over the whole cycle of the signal and in specific places. This only happens for signals of the same frequency - by definition.

 

[Lino]

Thanks Nugatory and Sophiecentaur. I understand the concepts / basics of the double-slit experiment, and why the configuration helps, but is this really a double-slit experiment (which I associate with the quantum wave / particle nature of light) or an experiment with two tightly confirned light paths / sources?

(I'm not questioning the experiment, just the reference to the double-slit experiment.)Regards,Noel.

 

[Nugatory]

Thanks Nugatory and Sophiecentaur. I understand the concepts / basics of the double-slit experiment, and why the configuration helps, but is this really a double-slit experiment (which I associate with the quantum wave / particle nature of light) or an experiment with two tightly confirned light paths / sources?

You're right, this is AN experiment that uses two slits, as opposed to THE double-slit experiment of QM. But they're connected by history: Setting up two slits is the traditional way of demonstrating interference phenomena in general, so was the starting point for considering quantum mechanical interference phenomena when people first started investigating them.

 

[Lino]

Ah! Now I understand. Much appreciated Nugstory.

Regards,

Noel.

 

[sophiecentaur]

If you want to predict what will happen with light then you only need to do the calculations for what would happen, classically, with radio waves. Adding the quantum factor is just standing up in a hammock afaics. Get the wave approach sorted out first and then, perhaps talk photons.
The wave approach says that two sources ('slits') will not produce a stationary spatial interference pattern unless they are coherent. This is the case, whether or not the two signals are a result of splitting one signal or they are generated independently. It would be a brave little Scientist who could predict a different result on quantum grounds.

 

[Lino]

Understood. Thanks Sophiecentaur.

Regards,

Noel.

 

[Emilyjoint]

DrDu has the main point. To produce observable/detectable interference sources must be COHERENT. The slits provide 2 coherent sources even from an incoherent single source.
Slits are not needed if lasers are used because lasers produce coherent radiation
Interference always occurs between waves of the same sort.
Interference is a property of waves, not slits

 

[Khashishi]

I think you can also get stationary patterns if one frequency is a rational multiple of the other frequency. It will require fast photography and well controlled light sources to see, but it should be possible.