Shouldn't the index of refraction change?

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Shouldn't the index of refraction change due to the random Brownian motion.
I watched a video recently that explained why light slowed down in different mediums and said that it was due to the fact that the light ray has to bounce off several particles before it leaves the medium its in.(Note that the light ray hits the particles at the speed of light)
But how can we have a constant index of refraction if we dont know how many particles the ray has to hit before it leaves the medium?!
 

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Change relative to what?
Index of refraction is a macroscopic material property, everything random that happens at the microscopic level averages out.
I watched a video recently that explained why light slowed down in different mediums and said that it was due to the fact that the light ray has to bounce off several particles before it leaves the medium its in.(Note that the light ray hits the particles at the speed of light)
That is just an attempt to explain the concept to non-physicists - it is not the actual physics, it is a model and it has many limitations. As an example, it cannot explain why light does not change its direction randomly in a material.
 

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