I What accelerates the light back to its constant speed?

[sibir1us]

TL;DR Summary

What accelerates the light back to its constant speed, when it changes medium?

what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

For example, let's suppose that there is a drop of water in vacuum. The light travels with the constant speed of light, then enters through the drop of water, decelerates, since the density is different, then it exits back to vacuum, supposedly traveling with the constant speed of light in vacuum.

There is a difference between the speed of the light in the medium of the drop of water, and the vacuum afterwards.

But the question is: what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

 

[javisot20]

TL;DR Summary: What accelerates the light back to its constant speed, when it changes medium?

The medium can change but light does not accelerate or decelerate, its speed is always c.

 

[PeterDonis]

what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

None. It doesn't take any energy, because the light is not "accelerated" after it exits the drop. See further comments below.

The medium can change but light does not accelerate or decelerate, its speed is always c.

While this statement is not false, it also leaves out the key missing piece that answers the OP's question.

The key missing piece is: the slower speed of light in a medium is only apparent. At a deeper level, what is happening is that light is being absorbed and re-emitted by the atoms in the medium, and that leads to an apparent slowdown in its speed, because we don't observe the individual absorptions and re-emissions. All we observe is their macroscopic effect: that it takes longer for light to cover a given distance through a medium than it does for it to cover the same distance through a vacuum, because although the light travels at $c$ between each emission and absorption, the emissions and absorptions take additional time. And since we can't see those individual microscopic events, we attribute that longer time it takes to the light traveling at a slower speed.

 

[PeroK]

TL;DR Summary: What accelerates the light back to its constant speed, when it changes medium?

what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

For example, let's suppose that there is a drop of water in vacuum. The light travels with the constant speed of light, then enters through the drop of water, decelerates, since the density is different, then it exits back to vacuum, supposedly traveling with the constant speed of light in vacuum.

There is a difference between the speed of the light in the medium of the drop of water, and the vacuum afterwards.

But the question is: what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

Although you've posted this under quantum physics, you can use classical electromagnetism to explain refraction, reflection and transmission of light waves using Maxwell's equations.(Mentor note: this thread has since been moved out of the QM subforum) to If A light wave travelling through one medium (vacuum, say) reaches the boundary with another medium, then some of the wave is reflected and some continues through the medium. The speed of the wave in the medium is determined by its refractive index. The total energy of the wave does not increase.

The same process happens when the transmitted wave exits the medium. Some of the wave is reflected back into the medium and some is transmitted into the vacuum. The speed of the wave in the vacuum is determined by Maxwell's equations and must be $c$. But, again, there is no increase in total energy.

In fact, the energy of the incoming wave will be greater than the total energy of the reflected wave plus the final transmitted wave. Some of the energy will have been absorbed by the medium.

The process of reflection and transmission at a boundary is covered in most undergraduate textbooks on classical eletromagentism. E.g. in Griffiths, section 9.3.2.

 

[Dale]

what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

First, how much energy is required to accelerate a massless particle to $c$? Once you figure out how much is required then you can start looking for what is missing that amount of energy.

 

[A.T.]

But the question is: what energy is used to accelerate the light to its constant speed in vacuum after it exits the drop of water?

I recommend the video below to understand what the change in speed of light in a medium means.



As for energy: The light that leaves the water has less energy, than the light that enters the water. So you should be rather asking where the energy went to, instead of where it came from.