# Light beams interfere when they cross paths?

According to this press article on Nature Update, second to last paragraph:

I’ve seen the photon self-interference diffraction patterns, but how does one make two separate light beams interfere with each other when they cross paths? I picture a grad student holding two flashlights pointing at each other, no interference there…

It depends: if you have two light beams in phase you get constructive interfernce and out of phase you get destructive interference, in other words the two waves add together linearly.

You must of seen the two-slit diffraction pattern where interference were the two beams of light coming from each slit causes light and dark bands.

‘superpose linearly’ would probably be a better description

When you hold two flashlights you do get interference but the light coming from flashlights is coming out at random phase and wavelength. If two photons that are exactly out of phase at at the same wavelength (I don’t know if I should say “photon” and “wavelength” in the same breath here) then they would cancel. But with conventional white light, the effects average out so you don’t see any interference effects.

Think about it - if a photon (a quantum of light) can interfere with itself, why couldn’t two photons, or a million, interfere with one another? This is one of those cases where light acts like a wave - when the peak of one wave is at the same place as the peak of another, the overall effect is a bigger wave. When the troughs align, you get a bigger dip.

The reason you don’t see it with two flashlights is that they are emitting white light - or something close to it, anyways. There are so many different wavelengths of light coming out of each flashlight, and the waves of the one are not necessarily in phase with the other, so the overall effect is that you don’t notice a discrete interference pattern - you basically get a continuous amount of light, although two flashlights shining in the same spot do seem brighter, don’t they?

The slit experiment, if you do it with a single light source and two slits, will give a diffraction pattern in which the light coming from one slit interferes with the light coming from the other. This is two beams interfereing with each other, as in your OP.

As for pointing two light sources at one another, I suppose if you knew the exact wavelength of light (say, of a laser) and calculated the distance between the sources, you could get them to interfere with one another…but I don’t know how to measure that.

I’m really not that much of a physicist, I just know as much as I just said (and I hope I even got that right!)

Please refer to my post in Doc Cathode’s old thread for a short primer on interference.

Photons have wavelength, in fact there really is no need to talk of photons as it may cloud the issue; two beams of light interfering with each other is simple classical physics.

Not exactly. If you have the same source shining on both slits, then it can be argued that that’s still just one beam interfering with itself.

And the problem with flashlights isn’t just that they’re white: A monochromatic source like a hot gas still won’t work. You need light that’s both monochromatic and coherent, which for most practical purposes means a laser.

I’m not sure if it’s just a sloppy expression or a misunderstanding, but light beams don’t really interfere when they “cross paths.” Interference is observable when two beams (or two components of a single beam) meet at a detector, i.e. both beams fall onto the same detector. Since light is a wave, two photons with opposite phase falling on the same spot on the detector will cancel out while two photons with same phase will add up.

But there is one beam of light shining across the room, and you arrange another light beam to cross it in the middle of the air, the first beam will not be affected. That is, the spot of light on the wall made by the first beam will not change. This is true even if you use laser beams.

p.s. By “detector” I mean anything that stops the light and allows you to observe the brightness of light at that point. A white piece of paper would do.