# Is the acceleration and deceleration of a wave instantanious?

When an light travels in free space, it has a velocity of propagation equal to the speed of light.

However, then the light enters a medium with a refractive index of n, the velocity of propagation changes to

$\ v_p = c / n$

Is this change in velocity instant? Or is there a gradual deceleration over distance, such as a ball rolling into a sand box (and acceleration when it exits the medium)?

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Inside a medium too photons will travel with same speed, but the "effective speed" will be low. – user10001 Jul 23 '12 at 20:25

Yeah, The resolution to this question is if you use a billiard ball type interpretation for atoms and light. In vacuum $c$ is always the same, so in between interactions with atoms, light travels at $c$ also. The "effective speed" noted above is a result of the decay time for excited states of atoms. So the light balls move between the atoms at $c$ and are held onto by the atoms for some time $\tau$ before released again. Thus light obtains an effective speed in a medium as a result of the finite excitation time for atoms in a medium. If you apply this situation at the interface of a medium and vacuum, the question becomes null. A change to the quanta perspective has these sort of perks. I hope this helps.