How can we derive or prove the priciple of optical reversibility from more basic principles?
It's based on experimental observation.
Experiment is the 'bottom line' in physics, which determines whether a basic assumption is true or false.
If by 'reversibility' you mean 'reciprocity', start here:
Then you'll be ready to read this:
I guess I meant something different. I am talking about the fact that, light traces back its traversed path if it is made to travel backwards.
For example, consider a glass surface which reflects and refracts some fixed amounts of the light ray falling on it from the air medium. So , a part of this ray is reflected back into air and a part of it is refracted into the glass plate.
Now if we reverse the direction of the light rays, i.e. let the two reflected and refracted rays, these two rays will travel backwards on the same path and will eventually combine to give the original light ray.
How can we prove this result?
You can't. (Maybe you could with great difficulty and ingenuity - but that's not the point)
We create experiments to test hypotheses in the simplest possible way.
It isn't necessary to test every possible situation to see if a principle holds 'in that particular situation'. Once it's been established, the point is taken as 'proved' (pending further refinement).
If I drive my car down the road at sixty miles an hour and don't brake at the end, I'll go off the road at the curve. I don't need to test the hypothesis.
There is plenty of evidence to suggest I should take care on the curve, as there is that the optical principle of reversibility holds.
Looking at the Fresnel-Kirchhoff diffraction formula- near the bottom of the page:
We see that it is symmetric; that is, a source point at Q will produce at the observation point P the same effect as a point source of equal intensity placed at P will produce at Q. That's the Helmholtz reversion theorem, or reciprocity theorem.
Alternatively, Fermat's principle can be used in which case there is no time or direction: the optical length is the shortest.
Or am I still not understanding your question?
Edit: When ultrashort pulses are involved, scattering behavior is very different than in the steady-state regime: IIRC, the far-field scattering pattern by an ultrashort pulse is very different than for constant intensities.
The links you posted went way over my head. I'm a freshman in college, and have hardly any prerequisites to deal with the stuff you're talking about.
Anyways, I'll store all these links and will visit them later on when I'm in a position to understand something.
I don't know if you can consider the following principle as more "basic" or not, but light rays obey the so-called Fermat principle: the path a ray takes to go from point A to point B is the one that minimizes the time of percurrence (remember that the speed of light in a medium is inversely proportional to the refraction index of the medium). From this principle you can deduce all the kinematics of light rays (whenever the "light ray" approximation is valid), that is, the laws of refraction and reflection. The time of percurrence to go from A to B is the same of the time to go from B to A, if the media of propagation are isotropic: if you see a point, that point sees you!
@metalrose: I think principle of optical reversibility is itself a basic principle, that can't be derived from something else.
@Petr Mugver: I don't agree with your reasoning.
First, it is limited to isotropic media.
Second, you haven't proved that the time it takes in one direction is equal to the time it takes in the reverse direction. Who said that the index of refraction is direction-independent? (As we all know, it isn't, but we know that from experiments only)
By the way, if A sees B, B doesn't necessarily sees A. This is a common mistake. Have you seen those security glasses? Although the path light takes is the same in the two directions, light intensities may be different.
The principle of optical reversibility is not valid for anisotropic media.
That's precisely the hypothesis of isotropic media.
Again, those glasses are made of a material that is not isotropic. I didn't make that assumption for nothing.
Separate names with a comma.