You can’t explain yourself? I followed your link. It looks like part of why half-silvered mirrors “work” for the purpose of seeing someone without them seeing you is that one side is kept brightly lit while the spying side is kept dark. I think “beam-splitter” is possibly a more accurate term for my question, which I looked up and found
Another design is the use of a half-silvered mirror. This is a plate of glass with a thin coating of aluminum (usually deposited from aluminum vapor) with the thickness of the aluminum coating such that part, typically half, of light incident at a 45 degree angle is transmitted, and the remainder reflected.
(Wikipedia)
Of course, this doesn’t actually explain anything—why should there be a thickness of aluminum such that part of the light is reflected while the remainder is transmitted?
Would a beam-splitter still work if the silvered and non-silvered parts were much larger (i.e. a chunky block pattern)? If you fired a single photon at that would it still make sense to calculate amplitude as you do in this post (considering the two outward paths and multiplying one by i, the other by 1)? Perhaps the distance between a silvered part and a non-silvered part needs to be close to the wavelength of the photon?
To answer your question as to how a half-silvered mirror works, first it might be a good idea to discuss how a full mirror works.
Classically speaking, the silver in the mirror has electrons that can freely move around. The electromagnetic fields of the incoming light accelerate the charged electrons in the silver, inducing electric current.
The currents flowing in the silver create their own electric fields, which by Lenz’s law, cancel out the electric field inside the silver, and in doing so, send an oppositely-shaped wave back out into the void (the reflected wave).
Because silver is not a perfect conductor of electricity, the topmost layer of silver does not completely cancel these fields, and so the light can actually penetrate a small distance into the metal (typically nanometers) before it’s finally converted into electric current.
If the silver coating is very thin, thinner than the penetration depth, then the component of the light wave that has penetrated through the metal will escape out the other side and keep going. That is, the resistance of the thin silver is high enough that the induced current doesn’t completely cancel out the electric fields of the photon.
This classical explanation is also the same as the quantum one.
They also make beamsplitters that are like you describe—I think they call them “Polka dot beamsplitters”. I don’t remember what they’re used for. They would work the same way, but if you have a focused laser beam, the beam spot would be so small that it would either hit a full-mirrored section or a transparent section, and not both. You would need to use a lens on both sides of the beam splitter to spread the beam out to encompass the whole beamsplitter, and then gather it back. I think as long as the polka dots are not on the same scale as the wavelength, it wouldn’t cause a problem.
If the cross-section of the photon was spread out so that it hit both silvered and non-silvered parts, some would reflect, yes. But it wouldn’t reflect quite like a mirror—diffraction effects would make things wonky, so people use half-silvered mirrors, which are nice.
How do they work, you ask? Did you ever take a course on wave mechanics where you calculated reflection and transmission coefficients? It’s exactly like that, except now the probability is essentially what’s “waving.” (if you haven’t, seehere)
You can’t explain yourself? I followed your link. It looks like part of why half-silvered mirrors “work” for the purpose of seeing someone without them seeing you is that one side is kept brightly lit while the spying side is kept dark. I think “beam-splitter” is possibly a more accurate term for my question, which I looked up and found
(Wikipedia) Of course, this doesn’t actually explain anything—why should there be a thickness of aluminum such that part of the light is reflected while the remainder is transmitted?
Would a beam-splitter still work if the silvered and non-silvered parts were much larger (i.e. a chunky block pattern)? If you fired a single photon at that would it still make sense to calculate amplitude as you do in this post (considering the two outward paths and multiplying one by i, the other by 1)? Perhaps the distance between a silvered part and a non-silvered part needs to be close to the wavelength of the photon?
To answer your question as to how a half-silvered mirror works, first it might be a good idea to discuss how a full mirror works.
Classically speaking, the silver in the mirror has electrons that can freely move around. The electromagnetic fields of the incoming light accelerate the charged electrons in the silver, inducing electric current.
The currents flowing in the silver create their own electric fields, which by Lenz’s law, cancel out the electric field inside the silver, and in doing so, send an oppositely-shaped wave back out into the void (the reflected wave).
Because silver is not a perfect conductor of electricity, the topmost layer of silver does not completely cancel these fields, and so the light can actually penetrate a small distance into the metal (typically nanometers) before it’s finally converted into electric current.
If the silver coating is very thin, thinner than the penetration depth, then the component of the light wave that has penetrated through the metal will escape out the other side and keep going. That is, the resistance of the thin silver is high enough that the induced current doesn’t completely cancel out the electric fields of the photon.
This classical explanation is also the same as the quantum one.
They also make beamsplitters that are like you describe—I think they call them “Polka dot beamsplitters”. I don’t remember what they’re used for. They would work the same way, but if you have a focused laser beam, the beam spot would be so small that it would either hit a full-mirrored section or a transparent section, and not both. You would need to use a lens on both sides of the beam splitter to spread the beam out to encompass the whole beamsplitter, and then gather it back. I think as long as the polka dots are not on the same scale as the wavelength, it wouldn’t cause a problem.
If the cross-section of the photon was spread out so that it hit both silvered and non-silvered parts, some would reflect, yes. But it wouldn’t reflect quite like a mirror—diffraction effects would make things wonky, so people use half-silvered mirrors, which are nice.
How do they work, you ask? Did you ever take a course on wave mechanics where you calculated reflection and transmission coefficients? It’s exactly like that, except now the probability is essentially what’s “waving.” (if you haven’t, see here)