Fresnel Diffraction

[reerer]

 

In Fresnel's paper, "Memorie su la Diffraction de la Lumiere" (1819), Fresnel describes diffraction using interfering light waves formed by the vibration of the elastic fluid (ether).

"21. If we call λ the length of a light-wave, that is to say, the distance between two points in the ether where vibrations of the same kind are occurring at the same time" (Fresnel, § 21).

"Admitting that light consists in vibrations of the ether similar to sound-waves, we can easily account for the inflection of rays of light at sensible distances from the diffraction body." (Fresnel, § 33).

"To understand how a single luminous particle may perform a large series of oscillations all of which are nearly equal, we have only to imagine that its density is much greater than that of the fluid in which it vibrates---and, indeed, this is only what has already been inferred from the uniformity of the motions of the planets through this same fluid which fills planetary space." (Fresnel, § 33).

"APPLICATIONS OF HUYGENS'S PRINCIPLE TO THE PHENOMENA OF DIFFRACTION

43. Having determined the resultant of any number of trains of light-waves. I shall now show how by the aid of these interference formulae and by the principle of Huygens alone it is possible to explain, and even to compute, all the phenomena of diffraction. This principle, which I consider as a rigorous deduction from the basal hypothesis, may be expressed thus: The vibrations at each point in the wave-front may be considered as the sum of the elementary motions which at any one instant are sent to that point from all parts of this same wave in any one of its pervious* positions, each of these parts acting independently the one of the other. It follows from the principle of the superposition of small motions that the vibrations produced at any point in an elastic fluid" (Fresnel, § 43).

 

Fresnel's diffraction mechanism is based on interfering light waves formed by the motion of Huygens' ether, composed of matter but diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism.

 

[Strange]

Yes, well done. There is no aether. We all know that. 

I assume you thought this would be controversial and cause people to get excited. But because you don't understand the material you are copying and pasting, you have shot yourself in the foot by confirming what is already known.

I'm afraid you have been found guilty of TWI (Trolling While Ignorant).

Time to move on.

[reerer]

Fresnel describes diffraction using spherical waves formed by the wave AMI (fig 7).

"In order to compute the total effect, I refer these partial resultants to the wave emitted by the point M on the straight line CP, and to another wave displaced a quarter of a wave-length with reference to the preceding. This is the process already employed (p. 101) in the general solution of the interference problem. We shall consider only a section of the wave made by the plane perpendicular to the edge of the screen, and shall indicate by dz an element, nn', of the primary wave, and by z its distance from the point M. These, as I have shown, suffice to determine the position and the relative intensities of the bright and dark bands." (Fresnel, § 53). 

Fresnel's expanding spherical waves are produced from points along the wave AMI when the bottom of the wave AMI touches the diffraction object. The expanding spherical light waves propagate to the diffraction screen and interfere forming the diffraction pattern but the creation of spherical waves away from the light source by the wave AMI is representing the wave front AMI as a light source that is arbitrarily generating spherical waves (energy) which violates energy conservation. Furthermore, Fresnel's interfering spherical waves that are used to represent the formation of the diffraction effect conflict with Huygens' propagation mechanism that spherical waves represented with partial waves KCL do not interfere.

[Strange]

3 minutes ago, reerer said:

Fresnel describes diffraction using spherical waves formed by the wave AMI (fig 7).

There is no "fig 7"

What is AMI?

What is CP?

What is dz?

What is nn'?

What is KCL?

Where did you copy that text from?

What is the point of this thread?

Carl? Is that you?

[John Cuthber]

On 10/26/2017 at 10:27 PM, reerer said:

 but diffraction forms in vacuum that is void of matter which contradicts Fresnel's diffraction mechanism.

Fresnel has been dead for nearly 200 years and is presumably past caring that his mechanism has been superseded.

 

Incidentally, if you cite the source- which I presume is this
https://books.google.co.uk/books?id=_L7LDAAAQBAJ&pg=PA155&lpg=PA155&dq=Admitting+that+light+consists+in+vibrations+of+the+ether&source=bl&ots=eShD3bnEPM&sig=_db4_zXKmUipVfHZ7-72PL_8kOc&hl=en&sa=X&ved=0ahUKEwivisnNlJbXAhWDXRoKHcLPAJYQ6AEIKDAA#v=onepage&q=Admitting that light consists in vibrations of the ether&f=false
 

then people can see what the **** you are on about

[reerer]

 

Fresnel derives a diffraction intensity equation by summating the interfering light waves' amplitudes, at the diffraction screen, using a line integral (equ 1).

"Hence the intensity of the vibration at P resulting from all these small disturbances is

 

 

 

{ [ ʃ dz cos (π z² (a + b) / abλ) ]² + [ ʃ dz sin (π z² (a + b) / abλ)]² }^1/2 "..................................1

 

 

 

 

(Fresnel, 53). Fresnel's derivation of the diffraction intensity equation is based on a line integral that represents the length of the wave AMI where dz is a segment of the wave AMI. Fresnel uses the line integral to summate the interfering light waves' amplitudes at the diffraction screen point P (fig 7) but the point P on the diffraction screen where the interfering light waves' amplitudes are summating is not within the limits of Fresnel's line integral (equ 1). In addition, during the diffraction effect of light, the crests and nodes of Fresnel's propagating light waves propagate in the forward direction. At the diffraction screen point P, the propagating light waves' amplitudes would oscillate forming an average resultant amplitude of zero, as time increases, that would eliminate the diffraction pattern. Furthermore, Fresnel is using the interfering light waves' amplitudes, at a point P, on the diffraction screen to represent the intensity (energy) of the diffraction effect which depicts a light energy that is dependent on the wave amplitude which conflicts with Lenard's photoelectric effect that proves light is composed of particles that light energy is dependent on only the frequency.

 

The formation of the small rectangular aperture diffraction pattern (fig 8) is represented using wave interference but the destructive interference of the light waves' amplitudes (energy) used to form the dark fringes of the diffraction pattern represents the destruction of the intensity of light; furthermore, the destruction of the light waves' amplitudes (intensity) would result in a reduction in the total light intensity of the diffraction pattern since the destroyed light waves' amplitudes do not contribute to the total light intensity of the diffraction pattern yet more than 80% of the small rectangular aperture diffraction pattern is composed of dark areas which would result in at least a 60% reduction in the total light intensity of the diffraction pattern yet experimentally, the total light intensity that enters a small rectangular aperture (dt = 1s) is equal to the total light intensity of the diffraction pattern. 

 

Fresnel is using spherical waves formed along the wave AMI to derive the diffraction intensity equation. The interfering spherical waves' maximum amplitudes are dependent on the inverse of the distance. The intensity formed by the spherical waves is dependent on I = (U)² where U is the equation of a spherical wave U = A cos(kr)/r. Using the distance r₁ = .1 mm where the spherical waves' maximum amplitudes are formed near the wave AMI, and, the distance of r₂ = 5 cm represents the distance from the wave AMI to the diffraction screen. The maximum total intensity of light formed by the spherical waves just after leaving the wave AMI, using cos²(kr) = 1/2, is I = [A cos(kr)/r]² = K/(.0001)² = K(10^-8), and, the total intensity at the diffraction screen is I = [A cos(kr)/r]² = K/(.05)² = K(2.5 x 10^-3); consequently, the total intensity at the diffraction screen decrease by the factor of 40,000 using Fresnel's spherical wave interference mechanism.