The speed of light in a medium and path integrals

[Seanra]

So I've heard from multiple sources that one explanation for why light slows down whilst traveling through mediums other than a vacuum is that the light "takes every possible path at the same time" through the medium.

Below I've drawn my two possible interpretations of what that means. Can somebody please explain which, if any, of my interpretations are correct?

http://imgur.com/WxPFga6

(Interpretation #1 is that every path it takes is the result of bouncing off electrons)
(Interpretation #2 is that it just takes completely random paths through the medium, doing loops and what not)

Cheers

 

[Simon Bridge]

So I've heard from multiple sources that one explanation for why light slows down whilst traveling through mediums other than a vacuum is that the light "takes every possible path at the same time" through the medium.

Please provide at least one reference for where you've heard this.
Otherwise we cannot tell what is intended or if it's just someone being wrong.
Neither diagram bears much resemblance to what is going on.

The particle approach to the passage of light through a solid is that it gets scattered off multiple centers - so takes a random walk.
The average path is the classical trajectory. Please watch these: all 8:
http://www.vega.org.uk/video/subseries/8