Optics B/C

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Re: Optics B/C

Post by blue cobra » August 5th, 2011, 1:07 pm

As I understand it, the energy of a photon is not continuous, but occurs only in discrete values. These values are described by Planck's constant in the equation E=hv. What I do not understand is how energy is quantized while frequency is not, or why frequency is quantized, and how exactly these relate to Planck's constant. Could someone please enlighten me?
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Re: Optics B/C

Post by ichaelm » August 5th, 2011, 3:12 pm

Think of it this way. We know the universe is relative, right? The relationship between space and time has no static 0 point. That is, in space, you can never say what your absolute velocity is, only what it is relative to another object. So time cannot be universally quantized, because its value depends on how it is observed. The minimum frequency for light emitted from a hydrogen atom is about 24 Terahertz, but I can also wave this pencil around at 2.4 Hertz and the universe can't stop me. So time is not universally quantized, and frequency is not universally quantized, and by extension, energy is not universally quantized. But that doesn't mean that in certain situations and certain reference frames it can't be quantized. In fact, both frequency and energy are quantized when you get really really close to a single proton, also known as a hydrogen nucleus. in that case, only very specific frequencies and energies of photons can be created. But it is silly to try and find a way to universally quantize frequency or energy, because if I shine a 400 THz laser at the moon, and then I fly towards the moon really fast, the beam is no longer 400 THz. Does this answer your question?

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Re: Optics B/C

Post by blue cobra » August 7th, 2011, 1:03 pm

Yes, thank you, I believe I understand now. I was erroneously assuming that E=hv as a mathematical relationship could only produce quantized values, whereas if we look at a hydrogen atom in an excited state moving to a lower energy state, it then becomes obvious how frequency becomes quantized within a certain reference frame. Thanks!
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Re: Optics B/C

Post by geekychic13 » August 20th, 2011, 2:10 pm

sooooooo, question. do we have to learn this for optics????
ichaelm wrote:Think of it this way. We know the universe is relative, right? The relationship between space and time has no static 0 point. That is, in space, you can never say what your absolute velocity is, only what it is relative to another object. So time cannot be universally quantized, because its value depends on how it is observed. The minimum frequency for light emitted from a hydrogen atom is about 24 Terahertz, but I can also wave this pencil around at 2.4 Hertz and the universe can't stop me. So time is not universally quantized, and frequency is not universally quantized, and by extension, energy is not universally quantized. But that doesn't mean that in certain situations and certain reference frames it can't be quantized. In fact, both frequency and energy are quantized when you get really really close to a single proton, also known as a hydrogen nucleus. in that case, only very specific frequencies and energies of photons can be created. But it is silly to try and find a way to universally quantize frequency or energy, because if I shine a 400 THz laser at the moon, and then I fly towards the moon really fast, the beam is no longer 400 THz. Does this answer your question?
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Re: Optics B/C

Post by Infinity Flat » August 20th, 2011, 2:33 pm

geekychic13 wrote:sooooooo, question. do we have to learn this for optics????
ichaelm wrote:Think of it this way. We know the universe is relative, right? The relationship between space and time has no static 0 point. That is, in space, you can never say what your absolute velocity is, only what it is relative to another object. So time cannot be universally quantized, because its value depends on how it is observed. The minimum frequency for light emitted from a hydrogen atom is about 24 Terahertz, but I can also wave this pencil around at 2.4 Hertz and the universe can't stop me. So time is not universally quantized, and frequency is not universally quantized, and by extension, energy is not universally quantized. But that doesn't mean that in certain situations and certain reference frames it can't be quantized. In fact, both frequency and energy are quantized when you get really really close to a single proton, also known as a hydrogen nucleus. in that case, only very specific frequencies and energies of photons can be created. But it is silly to try and find a way to universally quantize frequency or energy, because if I shine a 400 THz laser at the moon, and then I fly towards the moon really fast, the beam is no longer 400 THz. Does this answer your question?
Not exactly. You should know that light exists as both an electromagnetic wave and a quantized particle, the photon. You should also know that one common source of light (i.e. photons) is when the electrons around an atom jump from a high-energy excited state to a low-energy state, releasing the extra energy as a photon.

In regards to ichaelm's post, he is essentially saying that in order for the frequency/wavelength of an electromagnetic wave to be quantized (that is, occur only in discrete quantities,) space-time itself would have to be quantized. This is because if space-time were smooth (which we currently believe it to be,) then the Doppler effect (i.e. red-shift) would allow the frequency of an electromagnetic wave to change smoothly. Because we currently think that space-time is smooth, then the frequency and wavelength of a photon do not occur only in discrete values.
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Re: Optics B/C

Post by geekychic13 » August 21st, 2011, 12:43 pm

okay. i kinda understand, but not exactly. so we dont necessarily have to know that, but its related to something we have to know, right?
Infinity Flat wrote:
geekychic13 wrote:sooooooo, question. do we have to learn this for optics????
ichaelm wrote:Think of it this way. We know the universe is relative, right? The relationship between space and time has no static 0 point. That is, in space, you can never say what your absolute velocity is, only what it is relative to another object. So time cannot be universally quantized, because its value depends on how it is observed. The minimum frequency for light emitted from a hydrogen atom is about 24 Terahertz, but I can also wave this pencil around at 2.4 Hertz and the universe can't stop me. So time is not universally quantized, and frequency is not universally quantized, and by extension, energy is not universally quantized. But that doesn't mean that in certain situations and certain reference frames it can't be quantized. In fact, both frequency and energy are quantized when you get really really close to a single proton, also known as a hydrogen nucleus. in that case, only very specific frequencies and energies of photons can be created. But it is silly to try and find a way to universally quantize frequency or energy, because if I shine a 400 THz laser at the moon, and then I fly towards the moon really fast, the beam is no longer 400 THz. Does this answer your question?
Not exactly. You should know that light exists as both an electromagnetic wave and a quantized particle, the photon. You should also know that one common source of light (i.e. photons) is when the electrons around an atom jump from a high-energy excited state to a low-energy state, releasing the extra energy as a photon.

In regards to ichaelm's post, he is essentially saying that in order for the frequency/wavelength of an electromagnetic wave to be quantized (that is, occur only in discrete quantities,) space-time itself would have to be quantized. This is because if space-time were smooth (which we currently believe it to be,) then the Doppler effect (i.e. red-shift) would allow the frequency of an electromagnetic wave to change smoothly. Because we currently think that space-time is smooth, then the frequency and wavelength of a photon do not occur only in discrete values.
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Re: Optics B/C

Post by ichaelm » August 21st, 2011, 3:59 pm

You might be expected to know about stuff like that, but most likely you won't. It's up to the person writing the test. I've seen tests that went into the resolving power of a diffraction-limited lens, but for most of the tests I took the hardest topic was double rainbows. So unless you go to a hard state competition or nationals, you probably don't need to go that deep.

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Re: Optics B/C

Post by JSGandora » August 21st, 2011, 4:10 pm

Double Rainbows!?!? :shock:

Did you just need to know that it refracted once and reflected once for the primary rainbow and reflected again for the secondary rainbow? Or did you need to know more in depth?

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Re: Optics B/C

Post by ichaelm » August 22nd, 2011, 5:52 am

We just needed to know how they work and what they look like in certain situations. But if you know how the refraction works, you can derive the rest of what you'd need to know. It was a question in a test that Bayard Rustin made for some invitationals.

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Re: Optics B/C

Post by blue cobra » August 24th, 2011, 11:44 am

I understand qualitatively how the Doppler effect works, but I don't quite get how to do it quantitatively. Could someone please once again enlighten me?
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