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                                                                                                                                                                                                                                             THE BRAINS BEHIND THE DISCOVERY AND STUDY OF DIFFFRACTION                                                                        

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  • James Gregory.
  • Thomas Young.
  • Augustin-jean Fresnel.
  • Christiaan Huygens.
                                                                              DEFINITON

Diffraction occurs when light(beam/ray of light) or other system of waves such as (water waves, sound, electromagnetic waves ( 

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electromagnetic radiation), and small moving particles such as atomsneutrons, and electrons, which show wavelike properties) passes sharp edges or goes through narrow slits(aperture), the rays are deflected(spread out) and produce fringes of light and dark bands.

                                                                                                                                                                                      

                                                

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                                                                                                                                                                                                           Diffraction of light

                           

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Diffraction occurs when light(beam/ray of light) or other system of waves such as (water waves, sound, electromagnetic waves ( electromagnetic radiation), and small moving particles such as atomsneutrons, and electrons, which show wavelike properties) passes sharp edges or goes through narrow slits(aperture), the rays are deflected(spread out) and produce fringes of light and dark bands.

                                                                                                                                                                                      

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                                                                                                                                                                                                           Diffraction of light

                                                                                                                                                                                                                                                        EFFECTS OF DIFFRACTION

Diffraction effects are classified into either Fresnel or Fraunhofer types.

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Fraunhofer diffractionFraunhofer diffraction is the light-spreading effect of an aperture when the aperture (or object) is lit by plane waves, i.e., waves that effectively come from a source that is infinitely far away.

                                              

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                                                                                                                                                                         TERMS USED AND THEIR DEFINITIONS                                     Image Added
              

                                                                                        TERMS USED AND THEIR DEFINITIONS 

  • 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 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 : wave is a disturbance or oscillation that travels through space time, accompanied by a transfer of energy.
  • Fringes :the edge and outside boundary of something.
  • Interference*:{}interference* is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude.
  • Radiation:Radiation is energy that comes from a source and travels through some material or through space.
  • Frequency:is the number of occurrences of a repeating event per unit time.
  • Amplitude: amplitude of a wave is a measure of how big its oscillation is.

                                                                                                                                                                                     TYPES OF DIFFRACTIONS                                                   TYPES OF DIFFRACTIONS

  •                    Diffraction of light - is the bending                    Diffraction of light - is the bending of light as it passes the edge of an object.
  •                    water diffraction - is the diffraction of water waves passing through a slit. 
  •                    Sound diffraction - This ia a process whereby sound waves can diffract around objects,which is why you can still hear someone calling  even when hiding behind a tree.
  •                    Electron diffraction - Electron diffraction refers to the wave nature of electrons.Fast electrons are diffracted from a polycrystalline layer of graphite                 
  •                    X-Ray Diffraction - X-ray diffraction (XRD) is a tool for characterizing arrangement of atoms in crystals and distances between crystal faces. This can be used to identify atoms and the crystalline form
  •                    Powder Diffraction - Powder diffraction is a scientific technique using X-ray, neutron, or electron diffraction on powder or microcrystalline samples for structural characterization of materials.
  •                    Diffraction from a Single slit - The single slit diffraction is illustrated via the use of finite-difference time-domain (FDTD) simulation in which slits with various widths are illuminated by electromagnetic plane waves at a single frequency
  •                    Selected area diffraction - Selected area (electron) diffraction (abbreviated as SAD or SAED), is a crystallographic experimental technique that can be performed inside a transmission electron microscope (TEM)

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                                                                                                                        PRINCIPLES AND LAWS OF DIFFRACTION

                                                                                                                                      HUYGENS PRINCIPLEHUYGENS 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. 

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                                                                                                                          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.      

                                                                                                                                                   

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.         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.      

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

                                                                                                                                                   

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.

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                                                                                                                   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).

                                                                                                            

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                                                                                                 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

Constructive Interference of reflected waves (reflected waves in phase, i.e., maxima are superimposed).

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                                                                                                                   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).

                                                                                                            

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 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. 

                                                                                                                               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

                                                                                                                                             

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                                                                                                                                                 The derivation of Bragg's Law

                                                                                                                                             

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                                                                                                                                    http://skuld.bmsc.washington.edu/~merritt/bc530/bragg/

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Since AB = BC, then

nλ = 2AB

Recall that,  AB = d sinθ

Thus 

nλ = 2.d.sinθ

  AB = d sinθ

Thus 

nλ = 2.d.sinθ

                                                                                                                                                                             APPLICATION OF DIFFRACTION

There are several applications of diffraction and these are somewhat evident in our daily contact with objects exhibiting diffraction or diffraction properities, without we noticing,or on the other hand noticing the object but not knowing the principle behind it or what made the object look or act like that.

Here are some of the applications of diffractionare some of the applications of diffraction

                                                                                                                                                                                    SCIENTIFIC APPLICATION 

  1.  Diffraction is used a lot in discovering the structures of materials and atoms.
  2. It has been used a lot in discovering medicines and drugs.
  3. Diffraction is also fundamental in other applications such as x-ray diffraction studies of crystals and holography                                                                                       of crystals and holography                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               GADGET THAT USES OR WORK USING DIFFRACTION PRINCIPLES

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The hologram on a credit card,work with the principle of diffraction,as you can see we pay our bills through a credit card without noticing or caring to know how it works or on what principle is the credit card working on.Our cameras use the principle of diffraction,diffrication  in the apertures makes our pictures comes out sharp and clear.All these gadget we use every day or once since our existence and we dkont know how they operate or work.

                                                                                                                                                                         DIFFRACTION GRATING

 A diffraction grating may be either a transmission grating (a plate pierced with small, parallel, evenly spaced slits through which light passes) or a reflection grating (a plate of metal or glass that reflects light from polished strips between parallel lines ruled on its surface). In the case of a reflection grating, the smooth surfaces between the lines act as narrow slits. The number of these slits or lines is often 12,000 or more to the centimeter (30,000 to the inch). The ruling is generally done with a fine diamond point. Since the light diffracted is also dispersed (spectrum), these gratings are utilized in diffraction spectroscopes for producing and analyzing spectra and for measuring directly the wavelengths of lines appearing in certain spectra. The diffraction of X rays by crystals is used to examine the atomic and molecular structure of these crystals. Beams of particles can also exhibit diffraction since, according to the quantum theory, a moving particle also has certain wavelike properties. Both electron diffraction and neutron diffraction have been important in modern physics research. Sound waves and water waves also undergo diffraction. 

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                                                                                                 APPLICATION OF DIFFRACTION GRATING

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