THE BRAINS BEHIND DISCOVERING DIFFRACTION
*Italian scientist Francesco Maria Grimaldi originated the word "diffraction".He was the first to record accurate observations of the phenomenon(diffraction) in the year 1665. *
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- Aperture : Aperture is an optical terminology,it layman's term it is called different names such as an opening, hole, or gap.It often refers to an opening in which light is allowed to pass in optical systems such as cameras and lasers.
- Waves
- Fringes
SCOPE OF DIFFIRACTION
PRINCIPLES AND LAWS OF DIFFRACTION
HUYGENS PRINCIPLE
A Dutch physicist Christiaan Huygens earlier proposed in 1678, that "every point in which a luminous disturbance reaches act as a source of a wave spherical in nature", the summation of this secondary waves determines the form of the wave at any point in time".
Though his theory adequately explained how linear and spherical wave propagate, it didn’t explain how according to his own presumption these secondary wave move only in forward direction.
Image of Huygens wave refraction -- Image coursey of Wikimedia Commons
HUYGEN-FRESNEL PRINCIPLE
However, in 1816, French physicist Augustin-Jean Fresnel would argue that Huygens principle along with his own (principle of interference) can successfully explain not only the rectilinear propagation of light but also the effects of diffraction. To justify his claims he inculcated more arbitrary assumptions of secondary wave's phase and amplitude with and obliquity factor. His predictions were to some extend arrived at some agreement including the Arago spot, though with no physical root.
Image of Huygens-Fresnel wave diffraction -- Image coursey of Wikimedia Commons
Though a member of the French Academy, Poisson reviewed Fresnel’s theory and suggested that “a bright spot will appear in the center of the shadow of small disc" concluded that theory was insufficient. However in a counter analysis, another member of the same academy concluded after his investigations that Fresnel theory was indeed correct, his investigation was indeed helpful towards justifying the wave theory of light over the corpuscular theory.
The diffraction formula by Kirchhoff based on wave equation, gives a mathematical roots for diffraction. Fresnel assumptions that eventually led to the Huygens-Fresnel equation came from the derivation of Kirchhoff’s diffraction formula.
A good instance of this could be explained with a simple showing with two rooms with a common doorway. When sound is produced in one of the rooms, someone in the other room will assume the same produced sound in the next room is emanating from the doorway they share, as s/he view the doorway as the source of the source due to the vibrating of air at the doorway.
Now let’s consider a source at the point Po, with vibrating frequency f. The disturbance we describe as a complex variable Uo known as the complex amplitude, produces a wave with a wavelength λ, and wave number k = 2π/λ.
The complex amplitude of the primary wave at the point Q located at a distance ro from Po can be given as
THE PRINCIPLE OF BRAGG’S LAW
Sir William Lawrence Bragg in 1912 proposed a law that states that, diffraction occurs when electromagnetic radiation or subatomic particle waves with wavelength comparable to atomic spacing, are incident upon a crystalline sample, scattered by the atoms in the system and undergo constructive interference.
http://www.microscopy.ethz.ch/bragg.htm
Destructive interference of reflected waves (in the reflected waves, maximum and minimum of the wave amplitude are superimposed).
http://www.microscopy.ethz.ch/bragg.htm
Constructive Interference of reflected waves (reflected waves in phase, i.e., maxima are superimposed).
Mathematical form of Bragg's Law
nλ = 2.d.sinΘ
Where
• n is an integer determined by the order given,
• λ is the wavelength of x-rays, and moving electrons, protons and neutrons,
• d is the spacing between the planes in the atomic lattice, and
• θ is the angle between the incident ray and the scattering planes.
The derivation of Bragg's Law
http://skuld.bmsc.washington.edu/~merritt/bc530/bragg/
Taking into account the conditions necessary to make phases coincide when the incident angle equals the reflecting angle, the initial rays (incident rays) will be parallel and in phase with the point where the top beam hits the top layer at atom z. In the next layer, the second beam continues where its being scattered by the atom B. The second beam has to travel an additional distance of AB + BC for the two beams to move adjacently and in parallel to each other. The additional distance must an integral (n) multiple of the wavelength (λ) for the phases of the two beams to be the same:
Using pythagoras theorem,
AB/d= sinθ
AB = d sinθ
Since AB = BC, then
nλ = 2AB
Recall that, AB = d sinθ
Thus
nλ = 2.d.sinθ
APPLICATION OF DIFFRACTION
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