This principle is clearly counter intuitive. In using it mathematicians ignore part of the solution to the equations modelling it?
ure is the upper rather than the lower envelope of the secondary wavelets. Why does an expanding spherical wave continue to expand outward from its source, rather than re-converging inward back toward the source? Also, the principle originally stated by Huygens does not account for diffraction. Subsequently, Augustin Fresnel (1788-1827) elaborated on Huygens' Principle by stating that the amplitude of the wave at any given point equals the superposition of the amplitudes of all the secondary wavelets at that point (with the understanding that the wavelets have the same frequency as the original wave). The Huygens-Fresnel Principle is adequate to account for a wide range of optical phenomena, and it was later shown by Gustav Kirchoff (1824-1887) how this principle can be deduced from Maxwell's equations. Nevertheless (and despite statements to the contrary in the literature), it does not actually resolve the question about "backward" propagation of waves, because Maxwell's equations themselves theoretically allow for advanced as well as retarded potentials. It's customary to simply discount the advanced waves as "unrealistic", and to treat the retarded wave as if it was the unique solution, although there have occasionally been interesting proposals, such as the Feynman-Wheeler theory, that make use of both solutions.
We really need to look at the behaviour of mathematicians and scientists very closely in this regard, as Newton argued.
You will notice how the difficulties are finessed and obscured by mathematical notation and argumentation. By this kind of Browbeating they can obscure the obvious mismatch, and make fun of those who seriously argue that they or the formulation are " wrong"
The most obvious flaw is the exclusion of rotation. But of course if you can exclude half the result there can be little concern about excluding rotational arguments.
The second flaw is the switch to hyperbolic geometry. There is no proper transformationlal mechanism that ensures this has been done correctly. Normans course on hyperbolic geometry goes into detail about this kind of set up, and it is not trivial, nor impossible.
The additonal principle added by Fresnel also needs to be examined closely.
Fresnel is said to have mathematically demonstrated light as having no longitudinal wave mode. Thus he conceives of light as transverse oscillation only. His proof was the explanation of interference patterns with Arago's help using Polarized light. No longitudinal wave propagation component is not the same as light not propagating longitudinally. It means that light progresses without compression and expansion. Thus light progresses, according to Fresnel as a slab face , but that slab face rotates in all sorts of interesting patterns in the 2 d plane of the wave front.
When looked at as a spherical propagation, the transverse wave lies entirely in the spherical surface. This surface therefore is dynamically active like a bubble film, and tangentially or sphere surface oscillating rotating occurs, but no radial oscillation.
Fresnel researche reflectivity of transverse waves , and combined this with Huygens wavefront principle to explain lights wave behaviour, demonstrated by Tom Young. This detailed research needed to be done because the straight line ray was still dominating optics.
I have now come upon polarisation of reflected light, Brewster's Law and angle and Mahlus law.
Here prof Lewin derives Mahlus law by slight of hand, but that's ok because he " fesses up" and the law is ok anyway!
These behaviours and practices are what pass for good communication! I have to agree they are engaging, but if they are wrong they should be demonstrated correctly and 2 times as llong spent on ensuring the student understands the correction and why it had to be made?
Who said photons were relevant or even exist? There is much that masquerades as classical theory but in fact it is not classical theory. Rather it is a 5 th columnist for introducing newer concepts! This continues today. Old theories and results are quietly updated without ever being admitted as wrong or misleading. This is not science it is propaganda control, and damage limitation.
This gives the full modern picture, but is clearly a hybrid ased on quantum mechanical theory rather than solely on electromagnetic theory. I do not see a description of the electric or magnetic omponent changing orientation on reflection. There is however a lot of discussion of frequency and phase, none of which is very clear.
When I was young no one explained how a sine wave reflected off a boundary. Or represented a sound wave longitudinally . They just showed me a skipping rope! Once I was allowed to play a tuning fork, swing pendulums and set metronomes going. Tipped bodies to the edge of their stability point, just before they toppled and watched them rock. Spinning pennies and tops were allowed to run down. Nobody said to me: these are examples of waves, oscillations and vibrations, and part of concepts for sn undulatory theory.
Fresnel got hold of a diffracter and passed light through it. What was a diffracter?
The making of lenses and prisms revealed light could be focused or spread apart. This was first described as reflection, but then later observers realised that refraction was the more fundamental principle. But from the early days of lenses aberrations were experienced, notably" fringes" or fractures of light. Unlike the prism which separated light into colours , this seemed to be a clear splitting of light into lighter and darker colours, and mixes.
Grimaldi had noticed this pattern produced by pin hole cameras and around shadow edges from sharpened objects. They were called umbra and penumbra. When a light was not considered a pin point source the corpuscular explanation obscured diffraction. By introducing light through a pin hole Grimaldi revealed clearly that light itself was split apart "di" away from, "fractare" to split.
Now an object in a light beam clearly splits it, leaving a lightless region which falls as shadow. So what split a pin point light beam?
Grimaldi thought that light may come from the 2 edges of the pin hole, that is even an infinitesimal edge was a light source!
Newton was aware of Grimaldi s work when he demonstrated refraction in a prism.. Refraction means the bringing together of parts. Newton showed that white light was made up of parts. In that sense the size of the hole was irrelevant to making light partition. Light was already partitioned and what a lens did was combine those partitions ino white light.
"Di" separate , "fractare" partitioning.
Newtons view of light was different to his contemporaries. He could show light was partitioned by colour, and that a lens combined these partitions into a whole experience of white light. So how did a pin hole work with no lens? And in addition why did lenses also produce partitions in the light called fringere or fringes which means Fractions or partition!
It seemed that refraction did not eliminate diffraction, but Newton maintained there was no diffraction of light , it existed as fractions or corpuscles. These were combined into white light and or all the colours in our Sensorium, our faculty of perception.
So the issue for Huygens was how did light propagate, especially if it was in fractions and needed to be combined by refraction in a second lens, and why or how did a perfectly ground lens fail to combine the partitions in all regions. The corollary was how did a pin hole manage to focus like a lens that is Refract like a prism?
A pin hole should be small enough to select out a single ray. As a single ray it hold be a given colour if Newton was correct. Thus a single colour should shine on the wall in a pin hole camera. If we are generous and allow the rays to be randomly distributed then we should see the colour fluctuating or just a white patch.
The more Huygens thought about it the more difficulties he saw in the lineal transport of corpuscles model. Newton had assumed rays of corpuscles because he could separate them out in a prism. This he called dispersion. But the dispersion was constant. The rays did not appear to move about in the white light beam. The second prism recombined the partitions and the whole demonstration was of refraction! So why did a pin hole work like a lens and focus sn image with full colours?
In addition why did the images show the partitions around the edges like a lens?
Huygens conclusion was that Grimaldi was showing that a lense was like a diffracter ! A pinhole was not like a lens a lens was like a collection of pinholes! Light, whatever it was was too fine even for a pinhole to separate out individual fractions, but a fine array of "pinholes " so small could project and diffract all the rays spherically forward. Then somehow these diffracted forward rays would combine to form the light that falls onto the wall. The pinhole was too large to single out individual rays but large enough to let these mixed rays come through and be focused by some spherical lens like effect around the pinhole.
I do not think his ideas were easily understood by his contemporaries. His use of the wave metaphor was an attempt to give a practical demonstration of his ideas. But few were convinced nor studied his paper or his analysis or his phenomenological exemplars .
A diffracter was therefore a lens or a translucent material ground to enhance this light splitting. It was studied because lens makers wanted to know how to make the best lenses. The connection between Newtonian dispersion and Grimsldis diffraction was not made. Refraction was the main concept with Snell providing a quantitative way of measuring it. It was soon forgot that the angle of refraction was actually what Newton called the angle of dispersion! The angle of dispersion is precise the reverse of the angle of refraction on the other side of the prism. The only time dispersion came up was when the images had coloured rings showing the shape of the lens. These aberrations also included the diffraction patterns of Grimaldi. Thus Newtonian dispersion was identifiable with Grimaldis diffraction.
Newton observed it with Huygens, but could not explain it . Huygens theorised taht it could be due to light splitting from every point in space, and some parts adding up and other parts refracting out. But no one understood his concept, because he drew many spheres to show how sources could add up to a broad light front. Part of the front would advance the light while another part would retard the light. This he explained was like waves in water where the wave travels by advancing in the front and retarding in the rear.
How could this explain fringes?
He was not quite sure, but he thought that the eye received this mixture of intensities of light and somehow this caused light to be seen as "fringes" or partitions
No one really payed a lot of attention to his controversial theory because it was not possible to see these proposed variations in light, the "fringes" would have some explanation in terms of refraction and different focal points rather tha light actually being propagated in this way: advancing at the front retarding at the rear, and each point producing a spherical projection like Grimsldis pinhole.
Fresnel is the next person who looked directly at the diffracting lenses. They were perhaps not called diffracters, just bad lenses, but he studied the patterns they made and noted the way the light was bent around the lenses as well as through the lenses, he had no choice but to call the bending refraction if inside the lenses, but he could call it Diffraction if light was bent round or away from the boundary edge of the lens without light passing through the lens.
Apparently the breakthrough came when he introduced an opaque boundary within the area of the lens. He immediately saw that the light was diffracted by the boundary before or after refraction by the lens.
Now he could begin to design the first real diffraction gratings! Starting with one boundary then 2 abd then more boundaries in the lenses surfaces. He Also no longer needed to use bad lenses, and so he could now focus the diffracted light better!
Having established something "new" about light namely it could be fringed or diffracted and also focused He went on to use Snells laws to develop precise mathematical equations.
But how could this be explained?
Because Snells laws rely on the sine function he naturally considered the sine" wave " or rather the continuous sign function as a model. Using the sine function as a model he was able to plot when the sines interfered constructively and destructively.. This he was able to relate to the sine cycle length, and this varied for different diffracted colours.
Spectroscopy nd spectrometry was a new technology at the time but with Snells laws enhanced by Fresnels analysis it was able to take a great Leap forward. It required Arago to make the connection to waves and the Hugens advancing and retarding propagation as a wave, and further back,to Grimaldi
Huygens wave theory was not linked to a sine "wave " until Arago made the connection through Fresnels work. However Thomas Young had been attempting to explain light as a wave phenomenon and had derived similar but less detailed mathematical formulae. He at once recognised the utility of Fresnrls equations and Aragis relating it to Huygens theory , now forgotten. But it was the simple use of the sine function with different angular multiples, today called phases, that made Fresnels explanation definitive.
Poison merely argued a detail, but because of his fame Arago knew if he could demonstrate his own logic to have correctly predicted counter to his expectations, then Wave Mechanics was home and dry! And the universe was filled with an ether that undulated to carry light to and fro!
The discoverer of Polarized light was Mahli, a corpuscularist
Youngs story of rejection and triumph
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