How Is Huygens' Principle Derived from Basic Wave and Maxwell's Equations?

[ibc]

Hello

Does anyone know where can I find a derivation (or approximation) for Huygens principle from more "basic" principles? (i.e from the wave equation and\or Maxwell's equations)

Thanks

 

[mensa]

I guess you need Huygens-Fresnel principle.It's more essential,but I find it also a little hard to get through,expecially the math part

 

[ibc]

And where can I find that math part?

 

[mensa]

My mother tongue is not English,so I don't know where can you find it.
The only thing I know is that Huygens-Fresnel principle is in the diffraction part of light.I guess any optical book would include this.

 

[ibc]

I really have no idea what you're talking about (nor what it has to do with anybody's native tongue).
The Huygens-Fresnel principle is not just an expression to the diffraction of light, it's a way to characterize the wave in many circumstances.
What I'm looking for is the derivation for the principle from more basic ones.

 

[Prologue]

I really have no idea what you're talking about (nor what it has to do with anybody's native tongue).
The Huygens-Fresnel principle is not just an expression to the diffraction of light, it's a way to characterize the wave in many circumstances.
What I'm looking for is the derivation for the principle from more basic ones.

You asked where you could find it, mensa said he/she doesn't know because the place that he learned it from wasn't in english. Would you be satisfied if they referred you to a book in chinese if you had no knowledge of the chinese language?I believe it is more of an assumption, assume it is true and see what happens, then it agrees with experiment*. *I believe there are problems with the wavelets that make the approach not very logical. For instance, if everywhere along the wavefront it outputs spherical wavelets and that is what generates the other wavefronts, but what about the waves going backwards? They would generate new wavefronts on the back side of the existing wavefront and those would generate others, etc. So you are only really talking about the forward moving spherical part, which then seems arbitrary.

 

[mensa]

I'm sorry for not letting you get through,perhaps it's because my poor English.And thank you,Prologue,for the explanation.
I totally agree with Prologue's idea.What's more,I guess the book "A Briefer History Of Time" would help a lot,if have a lot of time to read it...In my mind Huygens-Fresnel Principle has lots to do with Quantum Theory,which allows light to travel in curve other than straight line.
I'm not sure if I am right or not,but I hope my words can help you.

 

[Claude Bile]

The Huygens-Fresnel principle can be thought of as taking a source (i.e. a wavefront) and dividing it up into an infinite number of point sources. So given a series of point sources you need two things to describe the evolution of a wavefront in time;

- Wave propagation (as defined by Maxwell's equations for an EM wave). This allows you to calculate the evolution of the wavelets.
- Superposition. This allows you to sum the wavelets to obtain your final wavefront, which is done via integration since there are an infinite number of them.

Does this answer your question ibc?

Claude.