You throw a rock into a lake, and it causes ripples. Throw another one into the ripples and that creates ripples, that change as they hit each other.
Sound blocking headphones create sound waves that cancel out the sound waves coming in,
Has this been studied for light, specifically visible light?
Yes, they have, famously in the Double-slit experiment.
Everything exhibits interference. Light is the least of it–electrons, atoms, kittens, etc. all exhibit interference as well (though it’s only been demonstrated with large molecules so far).
Holograms depend on it.
Optical interferometry is a huge part of lots of sensing and measuring technologies.
Right. But here’s what I don’t understand:
Turn on a blue laser. Now turn on a yellow laser, and orient the beam so that it passes through the beam of the blue laser. The yellow laser beam seems unfazed by the blue laser beam; after passing through the blue beam, it continues on its way like nothing happened. (Same can be said for the blue beam.)
Why don’t the changing electric & magnetic fields in the blue laser beam screw up the electric & magnetic fields in the yellow laser beam?
At low intensities, EM waves are linear. Two beams of light act as if the other doesn’t exist–although the fields merge, the math works out that they just don’t see each other. The only reason you ever see interference is because the beams (in the two-slit experiment) hit a screen–if the screen wasn’t there, the waves emanating from the two slits would continue on and deinterfere as they separated.
A very high intensities, EM is no longer linear, and you can have interference and other effects.
Because electric and magnetic fields both add linearly.
Is there a reason they don’t heterodyne?
They do, but you need a non-linear optical medium to make it happen. The most common application is in green laser pointers, which use a crystal to perform frequency doubling (the frequency is added to itself to give twice the frequency). Infrared laser light gets doubled to make green. But there are lots of other applications as well.
One big problem is that in order for you to see interference effects, the path difference between the two waves has to be shorter than the coherence length of the light. Light from any source is not a perfectly predictable set of sine waves. In a simple model, the waves appear to stop and start at almost random times, so that if you take a piece from a lobng distance away from another piece, the phase difference between them isn’t predicatable.
For ordinary light from the sun, or candles, or flashlights, or most common sources the coherence length is extremely short – on the order of a few wavelengths. That’s why Thomas Young’s double-slit experiment (referred to above) requires very narrow slits very close together, and will only show you a very few interference fringes.
When Dennis Gabor made the first holograms back in 1948 he used the source hhe could find with the longest coherence length – ultra-filtered single-wave light from a mercury source. Even so, the coherence length was on the order of a millimeter. His hologram couldn’t give you 3D holograms.
That all changed with the invention of the laser, which has, by comparison to anything else, enormous coherence length. If you do the double-slit experiment witha laser, yousee LOTS of diffracted orders. Supernumerary peaks in from a raindrop seem to go on forever, rather than the handful of supernumerary rainbows you see in nature. And Leith and Upatnieks were able to make holograms of objects tens of centimeter on a side, and they looked three dimensional.
It’s easy to produce interference from radio sources, or sound sources, or in water waves because the coherence lengths are huge and the phases are easy to align. Not so with light sources, even lasers. It’s easy to interfere a laser with itself (within the coherence length), but much, uch harder to interfere two different lasers, even of the same wavelength. The easiest way is to have both lasers "seeded " from the same source. But it IS possible to interfere two unconnected lasers. It’s just not at all easy. It’s even possible to interfere two lasers of different wavelengths, especially if the wavelength difference is tiny. This happens in Four-wave Mixing. Again, it’s not as trivial as just turning the lasers on and pointing them in the same spot. Your probability of seeing interference effects between a blue laser and an uncorrelated yellow laser if you just crossed the beams is about zilch.
Thanks for the excellent response. IANAP, so it will take a few readings to absorb it. 
You can do optical heterodyning, but you need a really strong signal – they didn’t do it until lasers were invented
Read up on “Coherence Length”. The Wikipedia article is all math, but you really need pictures to explain the concept to you
More picture here:
Some YouTube videos probably do a better job of explaining it, but I haven’t time to go through them. Try it yourself.
And then, when you understand Coherent Light and Incoherent Light, you can study Partially Coherent Light, and gradually drive yourself insane.
Or you can just whistle along with silverodeon music.
I first encountered the Heterodyne Boys when Phil Foglio did his limited run of Stanley and his Monster. I was convinced that this was a kinda forced joke about the Hardy Boys.
Nothing since has made me change my opinion. But I think that in Stanley’s mom we saw the first glimmerings of Agatha Heterodyne.
The speckle pattern characteristic of lasers is due to interference of the light.
You could though use the same laser and change the frequency of one beam. Yellow has about 1.25 the wavelength as blue, so you could probably use some frequency doublers/halvers and then four-wave mixing to produce (1+4)/4=1.25.
If you did it right, the two beams would share a phase relationship and you’d probably be able to observe interference under some conditions.
Yes, and it’s made possible by that long coherence length.
You can observe interference between waves differing widely in wavelength, but it isn’t easy.
Here’s a theoretical paper on it:
Raymer, M. G., S. J. Van Enk, C. J. McKinstrie, and H. J. McGuinness. “Interference of two photons of different color.” Optics Communications 283, no. 5 (2010): 747-752.
Sounds like they had more or less the same idea I had, using four-wave mixing to translate frequencies. Though I do like the concept of redshifting the light using a mirror traveling at relativistic speeds.