Diffraction

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Asuquo Uduak Peter
Kudaisi Mobolaji

THE BRAINS BEHIND THE DISCOVERY AND STUDY OF DIFFFRACTION

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.Here are the list of the scientist that has contributed in the study of diffraction

* sir Isaac Newton.

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 ( electromagnetic radiation), and small moving particles such as atoms, neutrons, 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.

Diffraction of light

EFFECTS OF DIFFRACTION

Diffraction effects are classified into either Fresnel or Fraunhofer types.

Fresnel diffraction is concerned mainly with what happens to light in the immediate neighborhood of a diffracting object or aperture, so is only of interest when the illumination source is close by.

Fraunhofer 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.

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 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

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)

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.

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.

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 P_o, with vibrating frequency f. The disturbance we describe as a complex variable U_o 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 r_o 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

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 diffraction

SCIENTIFIC APPLICATION

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

The effects of diffraction are usually seen in everyday life. One of the most evident examples of diffraction are those involving light; for example,when you take a keen look at a CD or DVD the closely spaced tracks on a CD or DVD act as a diffraction grating to form the familiar rainbow pattern.

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.

APPLICATION OF DIFFRACTION GRATING

Difraction gratings have several applications. Some of the applications includes:

1.SPECTROMETERS (devices which measure properties of light), MONOCHROMATORS (devices which only transmit rather narrow ranges of wavelengths of ELECTROMAGNETIC radiation chosen from sources which provide a greater range of wavelengths)

2.It's Application is also imminent in fibre optic communication (wavelength division multiplexing, to be more specific, which allows different wavelengths of light to carry different signals over a single strand of the optical fibre).

3.Hologram (holos-whole:gram -message) can be imagined as a complicated diffraction grating. The recording of a hologram involves the mixing of a laser beam and the unfocused diffraction pattern of some object. In order to reconstruct an image of the object (holography is also known as wavefront reconstruction) an illuminating beam is diffracted by plane surfaces within the hologram, following Bragg's Law, such that an observer can view the image with all of its three-dimensional detail.

4.lasers.

References

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