As a high school student, I was studying the dual nature of matter and radiation and wave optics. According to Planck's theory, the energy of a particle is given as hf where h is the Planck constant and f is the frequency. In wave optics I read that the frequency of light is invariant in different media, keeping the above two statements in mind we may infer that the energy of light is invariant across different media. However, in wave optics, I also read that light slows down by a factor of n (refractive index of a medium) in a medium. This means that despite light traveling relatively slowly it still has the same energy, which seems slightly absurd to me as a high school student. I know I am missing out on a piece of this puzzle, I just want to know what it is, where is the enrgy redistributed?
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$\begingroup$ Why do you think that moving slower will impact the energy? What relationship between energy and propagation speed do you have in mind? $\endgroup$– nasuCommented Apr 3, 2022 at 16:47
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$\begingroup$ @nasu I am aware of e^2=(pc)^2+(mc^2)^2, i suppose that's what you were expecting? $\endgroup$– Priyanshu ChoubeyCommented Apr 3, 2022 at 17:00
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$\begingroup$ I did not expect something special. Just curios what makes you think that there should be a reduction of energy in the medium. If you use this formula for light you end up with e=hf which has no dependence on velocity (p=hf/c for light and m=0), Anyway, these "c"s in the relativistic formulas should be the speed of light in vacuum, the universal constant and not dependent of the medium. $\endgroup$– nasuCommented Apr 3, 2022 at 17:35
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$\begingroup$ @nasu i again am aware of that but what is bothering me is that in a say in a glass slab light is traveling slowly but has the same energy as light traveling in vacuum which is moving faster and hence has comparitively greater kinetic energy this means that light in the slab has some other form of energy that compensates in for the lower kinetic enrgy to keep the total energy constant across diff. media $\endgroup$– Priyanshu ChoubeyCommented Apr 4, 2022 at 1:01
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$\begingroup$ And again, what makes you think that it has comparatively lower energy? The formula that you showed does not support this assumption. $\endgroup$– nasuCommented Apr 4, 2022 at 10:03
2 Answers
When an EM wave enters a transparent material there is an electromagnetic wave produced inside the material. This wave interacts with the transparent medium to produce mechanical effects, like forces, momentum, stress, etc.
Unfortunately, there is no one unique way to separate the field momentum and energy from the material momentum and energy. When an EM wave enters a transparent medium the total energy and momentum are conserved, but the field energy and momentum are not. The rest of it goes into the matter, regardless of the exact method chosen to determine the field energy and momentum.
This is discussed by Pfiefer et al. in https://arxiv.org/abs/0710.0461 , but it is definitely at a college level rather than a high school level.
I can relate the question to this, In my answer there you can find an equation : $$\text{Power}\propto A^2 \text {v} \tag{1}\label{1}$$
As you can see in the following image that, if there is changes in frequency and wavelength then light "color" will be changed. But in reality, when light from a medium enters another medium then the "color" remains constant (they totally doesn't change, ignoring the effect of water, for water medium).
From the equation $\eqref{1}$, you can see that velocity is proportional to power (energy per unit time, now taking $t=1 \ \mathrm s$, and calling it energy rather than power). Since velocity is changing in different medium but if the energy remains constant then amplitude increases or decreases depending on velocity.
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$\begingroup$ This is not true. Shorter wavelength means higher energy of photons. x-ray have shorter wavelength than visible light. $\endgroup$– nasuCommented Apr 3, 2022 at 16:45
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$\begingroup$ @nasu Ow! Yes. I have rechecked it. I will edit, I am busy little bit and have some confusion so planning to edit the answer later. deleting it for now.... $\endgroup$ Commented Apr 4, 2022 at 6:05
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$\begingroup$ The velocity in a medium is independent on power or energy, at least for linear phenomena. The power depends on the elocity but velocity is a property of the medium (and wavelength). It is like the mass of an object depends on his density of the materia. But the density is the same for any object made from that material. You can write $m \propto \rho $ but it would be silly to say that density of copper depends on the mass of a specific copper object. $\endgroup$– nasuCommented Apr 5, 2022 at 15:51
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1$\begingroup$ No, it should not necessary change. The medium may absorb some energy but that energy is gone, does not belong to the light wave anymore. In a transparent medium the speed may change sinificantly (like by a factor of 2/3 in glass) whereas the absorption is almost negligible. The energy per photon anyway depends on frequency only and this does not change in the medium. The propagation of light in transparent media is actually complicated, being a collective interaction. But the change in speed does not imply a change in energy. You have the same intuition as the OP but no justification. $\endgroup$– nasuCommented Apr 6, 2022 at 3:40