# Huygens principle incomplete?

• marts
In summary, the obliquity factor is a limiting case of Kirchhoff's theory that accounts for the behaviour that we see. Kirchhoff's theory is more complex, and includes sources that don't produce secondary waves isotropically.

#### marts

Hi all

"The Huygens-principle recognizes that each point of an advancing wave front is in fact the center of a fresh disturbance and the source of a new train of waves; and that the advancing wave as a whole may be regarded as the sum of all the secondary waves arising from points in the medium already traversed." (source: Wikipedia)

Applying this principle would mean that that the light coming from a source (eg. a laser) quickly spreads out even behind the source. One would also expect to see inteference-patterns on a screen placed behind and not infront of a double-slit.
Obviously this is not the case (or is it??).

So is there any extended huygens-principle which describes at which angle the elementary waves emit or that gives some other explination??

obliquity factor

marts said:
So is there any extended huygens-principle which describes at which angle the elementary waves emit or that gives some other explination??
Absolutely! Fresnel, who extended Huygens's principle into the Huygens-Fresnel principle, recognized the need for an angular dependence of the secondary waves. Kirchhoff nailed it down, defining an obliquity factor = $(1/2)(1 + \cos\theta)$. The angle is with respect to the normal of the primary wavefront. This eliminates the bogus "backwards" wave. (Look up "obliquity factor" in any decent optics book for more.)

This very issue drove me nuts when I was first learning about Huygens's principle. So I feel your pain.

Thanks Doc Al, that really sets my mind free again.

I had been searching for days without any descent result, so I didn't expect to get such a quick and precise answer at all.

Hi there.

Interestingly, the introduction of the obliquity factor is an ad-hoc fix by Fresnel.

In 1886 Kirchoff gave a full mathematical description which accounts for the behaviour that we see. The obliquity factor falls out of this theory as a limiting case.

Within Kirchoff's theory, there are two types of source, and so the simplicity of Hugens' principle is lost. In addition, there is no physical analog for Kirchoff's sources...

All in all a very fascinating problem. I'd recommend reading this paper:
http://www-ee.stanford.edu/~dabm/146.pdf

Or D. Miller, "Huygens’s wave propagation principle corrected," Opt. Lett. 16, 1370-1372 (1991). if the link doesn't work.

Good luck!

I always wondered how this affects the explanation of reflection.

If you consider the reflection line representing the mirror, actually none of the physical properties of a mirror enters the proof at any point. The proof therefore applies to any imagined line.

So why aren't there reflected waves all over the place?

How does this change for real waves? What I mean by real waves is something like water waves, where there is actually something that is vibrating, so that the sources on the wave-front are real: do these sources generate secondary waves that are isotropic?

Take 2-slit diffraction of water waves. The screen blocks the waves, but the slits can be seen as sources for a new wave because there is actually water at the slits that vibrate (like dipping your finger in a pond at the slits). Do the water at the slits generate backwards waves?

RedX said:
How does this change for real waves? What I mean by real waves is something like water waves, where there is actually something that is vibrating, so that the sources on the wave-front are real: do these sources generate secondary waves that are isotropic?

Take 2-slit diffraction of water waves. The screen blocks the waves, but the slits can be seen as sources for a new wave because there is actually water at the slits that vibrate (like dipping your finger in a pond at the slits). Do the water at the slits generate backwards waves?

## 1. What is Huygens principle incomplete?

Huygens principle is a theory in wave optics that states every point on a wavefront can be considered as a source of secondary spherical wavelets. These wavelets then combine to form a new wavefront. However, this theory is incomplete as it does not fully explain the behavior of light in all situations.

## 2. What are the limitations of Huygens principle?

Huygens principle cannot fully explain the diffraction of light around objects with sharp edges or slits, as well as the interference patterns observed in double-slit experiments. It also does not take into account the polarization of light.

## 3. How did Huygens principle lead to the development of wave optics?

Huygens principle was one of the first theories to explain the propagation of light as a wave. It laid the foundation for the development of wave optics, which has greatly advanced our understanding of light and its behavior.

## 4. Can Huygens principle be applied to all types of waves?

Huygens principle was originally developed for understanding light waves, but it has since been applied to other types of waves such as sound and water waves. However, it may not be applicable to all types of waves, especially those with complex behaviors.

## 5. How has the understanding of Huygens principle changed over time?

Since its initial formulation, the understanding of Huygens principle has evolved and been refined through further experimentation and theoretical developments. Its limitations have also become more apparent with the advancement of technology and the ability to observe light in more detail.