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I've been studying geometric optics and I'm still a little confused with this idea of light ray. In the book I'm studying everything is being done starting from Fermat's principle which states that the ray path is the one which extremizes the optical length.

Now, I thought that because of this, geometric optics viewed light as particles and I thought that a light ray then would be a trajectory of those light particles. But my question here confirmed that geometric optics doesn't care if light is made of particles or waves.

On the other hand, if we think of light ray as "the path taken by light between two points", this is no good, because the idea of trajectory in this sense is not well defined for waves. Indeed, this idea of light ray doesn't even seen clear to me, because as we know if we have some light source, the light doesn't go along one single path, but as a wave it spreads out in all of the directions at once.

So, if geometric optics doesn't care about if light is made of particles or waves, what really is a light ray? How should we understand light rays and ray paths?

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In a wave picture we can put an arrow at each point of the wave that points in the direction of propagation which is (normally) at right angles to the wavefront. If we string a bunch of these arrows together into a line, we get a ray.

I tend to think of this as being analogous to field lines in electromagnetism. In fact you can take this analogy a bit further and see that wavefronts are behaving a lot like equipotentials and the phase of the wave is playing the part of voltage.

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Light rays are orthogonal trajectories to the phase fronts. A phase front is an equal phase surface of a propagating wave, so the rays are lines perpendicular to these surfaces. It is a fundamental law of geometric optics (theorem of Malus and Dupin) and is effectively equivalent, at least in an isotropic medium, to all other formulations of it (Snell's law, Fermat principle, etc.) that the rays and phase fronts stay orthogonal after any number of reflections and refractions. See: https://books.google.com/books?id=oV80AAAAIAAJ&pg=PA139&lpg=PA139&dq=malus+dupin&source=bl&ots=y0Q_wWTYMF&sig=quQxS2fvhgCw_xi6Zeh1pcdf1Jk&hl=en&sa=X&ved=0CDYQ6AEwB2oVChMIq9a8x6umxwIVxlw-Ch3y4wB4#v=onepage&q=malus%20dupin&f=false

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