Question about Huygen's principle

I think the point to remember with Huygen's principle is that it is a tool to find the shape of a scattered wave at a later stage.

Secondly the light from a torch is diffracted and the wavefronts are certainly not parallel since the light source is extended. You'll probably have noticed that if you shine the torch on a wall then the circular image on the wall will be of a greater diameter than the torch aperture. That's because the light is spreading out. There'll also be something that looks like a faint airy disc pattern.

 

Yes but its the envelope of those wavelets that represents the wavefront at a later time.

 

Hi yoran!

Think of two concentric spheres, with a point source at the centre.

The light spreads out to reach the inner sphere, then every itny area on the inner sphere has only a tiny proportion of the original energy, which it then re-radiates according to Huygen's principle, but all the re-radiation still reaches the outer sphere (except for the inward half of the re-radiation, which cancels out completely!)

So no increase of energy.

 

I think that the Huygens principle doesn't result in infinite energy because when each point becomes a new "source", waves "generated" by adjacent points will actually tend to cancel each other out due to interference.

However I am really not so sure I understand the principle very much. I am still unconvinced that Huygens is the explanation for DIFFUSION of waves. It sounds to me like it's true only when matter is present, but not in a vacuum.
For an acoustic wave, you can say that Huygens is the reason why you can hear a sound without having a straight path from the source (without air or matter the idea doesn't apply because sound wouldn't propagate at all).
For a light wave that's also possible but only if you have air... in vacuum you cannot see beams of light "from the side". You can see the whole beam produced by a torchlight, going from the torchlight to the wall, because of the particles in the air, but if you were in a vacuum you would only see the illuminated portion of the wall (and the torchlight's exit point itself if you have line-of-sight with it) but you will not see the beam between the torch and the wall.

 

Does it really explain them?

 

Huygen's priciple does not violate the conservation of energy, nor does his construction require that all light emission be pefectly spherical waves.

Goodman, in "Introduction for Fourier Optics", as a good discussion about this point.

Huygen's idea was entirely intuitive when he proposed it in 1678, and was based on an idea on how to construct wavefronts. Fresnel, in 1818, added some arbitrary assumptions regarding the subsequent amplitudes and phases of these secondary sources, and as a result, was able to calculate diffraction patterns with some accuracy. These assumptions, which were additionally developed by Kirchhoff, were shown to be mutually incosistent with each other by Poincare and Sommerfeld in 1892/1894. Therefore, the Huygens-Fresnel principle and subsequent Rayleigh-Sommerfeld diffraction theory can only be considered a first approximation to light scattering.

The most important simplification is that light is treated as a scalar field, and that the electric component is independent of the magnetic component. The scalar diffraction theory yields accurate predictions under two circumstances:

1) The aperture is much larger than a wavelength
2) The diffracted fields are not observed close to the aperture.

There are a lot of complexities to consider- radiometry, the thermodynamic basis of optics, is not well-defined mathematically, leading to many odd effects- the spectrum of light can change with propagation, for example.

 

Thanks for the insightful post!

Doesn't diffraction actually require the opposite condition (aperture small, comparable to wavelength)? I just wonder if Huygens principle really helps explaining diffraction (an refraction) at all...

 

No. You may be thinking of using thin slits to obtain interference patterns, or to exaggerate the far-field diffraction pattern. The first (interference) uses thin slits to increase the coherence state of light, which is required to obtain good quality fringes.

Also note that the Rayleigh-Sommerfeld (and Fraunhofer) diffraction theory discusses the *fields*, while your eyes observe the *intensity*. That can also be significant, especially when considering interference effects.