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After all, it does change direction when reflection occurs. So shouldn't it also accelerate? And since the acceleration cannot increase the speed of light, mustn't it slow down?

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Possible duplicate: – Qmechanic Jan 23 '13 at 23:41
Maybe this minute physics video would be helpful for now. Light doesn't have to slow down necessarily :-) – Waffle's Crazy Peanut Jan 24 '13 at 3:50
up vote 4 down vote accepted

Light does not slow down during a reflection.

Light is a signal disturbance in electric and magnetic fields. These disturbances propagate through space at a fixed speed $c$ in vacuum. The situation is completely analogous, in a mathematical sense, to a wave pulse that is sent along a string. When the pulse encounters a boundary, it flips direction, and may or may not change phase depending on the type of boundary encountered. For good graphical depictions of this phenomenon, visit this page.

If you emit a pulse of light at a distance of 1 meter from a plane mirror, and measure the amount of time it takes for the signal to return, you will find that it is 2 meters / $c$, neglecting refractive effects of the air. In this sense, we say that the light has not slowed down, even though it has changed direction in the middle of its journey.

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Light changes energy during reflection or refraction. However it maintains its constant speed. The change in this energy is detected as a change in the frequency and/or wavelength.

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There are some processes which may be termed acceleration. For example a photon having velocity $c$ in vacuum and then having velocity $c/n$ after entering a medium with refractive index $n$. Or as you describe, a change from velocity $c$ to $-c$ when reflected from a mirror. However, the magnitude of it's velocity is $c$ at all times, and in fact in when changing medium the photon is absorbed and a new one emitted, so whether that is to be called an actual acceleration is debatable. This queston is related and may be of interest.

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The actual thing that happens, in a more general way than just reflection, is that when the space properties change, for example, a mirror, the particles of the mirror absorb the photons, and emit new ones, the light doesn't reflect but dissapears giving energy to the atoms that then loose it again as a new photon. In an interface of materials, when light passes from $c/n_1$ to $c/n_2$, the same thing happens, the light is absorbed and re-emited by all the particles, and it actually travels at speed $c$ between them, the average behaviour of the wave front is that it travels a little bit slower, when actually the light is not travelling directly in the direction of the wave front, but average.

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