What happens to a light photon when it hits glass?

[askbbj]

Homework Statement

Using quantum mechanics, what happens when a photon of light hits glass?

Homework Equations

Momentum= Mass x velocity

The Attempt at a Solution

I am not sure of my answer but suffice to say the following:
Assuming the collision between the photon particle and those in the glass is inelastic, then going by the conservation of momentum, we can say that the total momentum before the collision is the same as that after. If that is the case, then the total energy before is the same as that after since energy is propotionate to momentum. But I also understand that the speed of light slows down in glass. So if this is the case, it contradicts what I had said earlier about the energy of light being constant throughout. Anyone who begs to differ in opinion?

 

[jbriggs444]

If that is the case, then the total energy before is the same as that after since energy is propotionate to momentum.

Come again? Energy is not proportional to momentum. Consider, for instance a reference frame in which total momentum is zero before and after the event.

 

[haruspex]

Using quantum mechanics

Where in your reasoning have you done that? (Not saying you haven't, just asking.)

Assuming the collision between the photon particle and those in the glass

Collision?

total momentum before the collision is the same as that after.

What about the momentum of the glass.

Energy is not proportional to momentum.

Well, for a photon E=pc, no?

This thread looks relevant: https://physics.stackexchange.com/questions/44509/photon-energy-momentum-in-matter

 

[collinsmark]

Quantum mechanically speaking, what is the relationship between the photon's energy and its frequency? (Hint: historically, this is one of the very first relationships* that ushered in quantum mechanics.)

Does the photon's frequency change when it enters the glass?

*[The relationship I'm speaking of was originally discovered by Max Planck, but it was Albert Einstein that really nailed the significance of it in one of his 1905 papers (he published several papers in 1905; this was one of them).]

 

[jbriggs444]

Well, for a photon E=pc, no?

Sure. But the line of reasoning had to do with momentum conservation for the whole system, not just the photon. If we adopt a frame where system momentum is zero and if energy were proportional to momentum it would follow that system energy is zero. But energy is non-negative for each system component separately. To achieve a total energy of zero, the photon energy needs to be zero (no photon) and the glass energy needs to be zero (E=mc^2 -- no glass either).

 

[haruspex]

Sure. But the line of reasoning had to do with momentum conservation for the whole system, not just the photon. If we adopt a frame where system momentum is zero and if energy were proportional to momentum it would follow that system energy is zero. But energy is non-negative for each system component separately. To achieve a total energy of zero, the photon energy needs to be zero (no photon) and the glass energy needs to be zero (E=mc^2 -- no glass either).

I was just suggesting that’s where askbbj got that idea from.

 

[askbbj]

Homework Statement

Using quantum mechanics, what happens when a photon of light hits glass?

Homework Equations

Momentum= Mass x velocity

The Attempt at a Solution

I am not sure of my answer but suffice to say the following:
Assuming the collision between the photon particle and those in the glass is inelastic, then going by the conservation of momentum, we can say that the total momentum before the collision is the same as that after. If that is the case, then the total energy before is the same as that after since energy is propotionate to momentum. But I also understand that the speed of light slows down in glass. So if this is the case, it contradicts what I had said earlier about the energy of light being constant throughout. Anyone who begs to differ in opinion?

Hi is a light photon consist of all the wavelengths in a spectrum?

 

[haruspex]

Hi is a light photon consist of all the wavelengths in a spectrum?

No, it will have just the one wavelength.

 

[collinsmark]

Hi is a light photon consist of all the wavelengths in a spectrum?

No, it will have just the one wavelength.

Haruspex is correct. @askbbj, are you able to answer my question about the relationship between a photon's energy and its frequency?*

*(This is the hint question about Albert Einstein's 1905 paper. Another hint: it's the same paper for which he won the Nobel Prize.)

 

[Cthugha]

No, it will have just the one wavelength.

Please do not write that. It is convenient, but not correct. I know that this is usually written in a simplifying manner to help students learn, but most students have a hard time unlearning it afterwards. The typical Fourier modes in the decomposition of a light field into harmonic oscillators are monochromatic. This is why you do this decomposition. However, these modes are not the definition of what a photon is. Single photons do not need to be monochromatic. In fact, no real single photon source is even close to that. A single photon may be spectrally narrow or broad. This is not a defining element. You just need the photon number to be 1 in your basis of choice. It is also a very common practice to spectrally tailor single photons (see e.g. https://iopscience.iop.org/article/10.1088/0034-4885/75/12/126503/meta or https://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.165310).

Getting back to the initial question: The transmission of light through a medium is nontrivial, but usually, this question does not aim at momentum conservation, but about how to interpret the fact that the photon may only be transmitted or reflected as a whole. There is no 96% transmitted and 4% reflected photon. What does this imply to you?