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A straight look at Diffraction

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6 Oct 2007 19:23:34 IST
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6 Oct 2007 19:23:34 IST
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A straight look at Diffraction
Engineering Entrance , JEE Main , JEE Advanced , Physics , Optics , Modern Physics

# A straight look at Diffraction

A deeper look into the field of diffraction. This phenomenon has been studied for a long time by prominent scientists like Issac Newton and Huygen. A little more about the diffraction theory and its history, with examples that make us more aware of this field.
Light is normally considered to be traveling in straight lines, and for all practical purposes it does. Because of this property, any obstacle in the path of light casts a shadow. If light travels exactly along straight lines, the shadow must have the exact geometric shape of the obstacle. On closer examination, however, it is found that even the sharpest shadow is blurred slightly at the edges. This happens as a result of the small bending of light around the sharp edges of the obstacle, known as diffraction.

It is a common experience that two close objects- like two letters of the alphabet in fine print, which can be distinguished at normal reading distance- cannot be seen as separate at greater distances. This effect is a result of diffraction, which is defined as "The study of geometric optics is built on the assumption that in a homogeneous transparent medium, light travels in a straight line. But deviation of light (as in bending) around sharp edges is called diffraction". When a millimeter ruler or two lines drawn on a paper with one millimeter separation are viewed at increasing distance from the eye, the lines become blurred together and are thus unresolved at a distance of about 3 meters or 3,000 millimeters. Thus, for the human eye directly looking at the lines, the angular resolution limit is about 1/3,000. The diffraction limit of angular resolution of the human eye is given by the angular size of the image spot on the retina from an incident plane wave emitted by a distant point source. When this is calculated from the diameter of the pupil of the eye (width of the circular aperture) and the mean wavelength of the incident light (about 550 nanometers), it is found to agree with the angular resolution limit calculated with a millimeter ruler. Hence, the limits of resolution of the eye are understood on the basis of the diffraction phenomenon by treating the pupil of the eye as a circular diffraction aperture and the retina as a screen. The same idea is applicable to the resolving power of an astronomical telescope, where the objective lens acts as the diffraction aperture.

The diffraction effect is common to all radiations that propagate in the form of waves. Radio waves and sound waves bend around obstacles quite a bit a person cannot be seen behind a screen, but can hear that person talk. The bending effect depends on the wavelength of the radiation under consideration. The wavelength is the combined length of a wave crest trough. The greater the wavelength, the higher the bending will be. The length of radio waves is of the order of hundreds of meters. Hence, radio waves can bend easily around even buildings, as they are not too big. On the other hand, the wavelength of light is less than a millionth of a meter; therefore, light bends around sharp edges only by a small amount. When one looks at a distant street lamp through a tiny curtain, some interesting patterns can be seen around the lamp, which are caused by diffraction.

The understanding of the Physical nature of light was the pursuit of many eminent physicists in the seventeenth and the eighteenth centuries. In the seventeenth century, Sir Isaac Newton and Huygens pioneered two different theories for the nature of light. According to Newton, light is of Particle nature, whereas Huygens viewed light to be in the form of waves. This controversy raged for nearly three centuries until the advent of quantum electrodynamics, which reconciled the arguments with the wave particle duality of light. The diffraction phenomenon can be accounted for only on the basis of the wave theory of radiation. Therefore, the development and understanding of the subject through the important works of scientists such as Fresnel, Fraunhofer, Kirchoff, and others gave strong support to the wave theory. The wave theory was developed further by James Clark Maxwell, who showed that light is in form of electromagnetic waves. These waves are made up of an electric component and a magnetic component; these components are locked in step at right angles to each other and fluctuate together.

The study of the diffraction phenomenon marked the defects in image formation and the limitations of the optical instruments in this regard. It also led to the construction of new astronomical telescopes with huge objectives, which led to enormous progress in the field of astronomy. The development of the optical diffraction grating and its extension to the X-ray diffraction and crystallography is one of the greatest contributions to the advancement of science. All solids can be classified as crystalline or amorphous, and there are more than twenty thousand crystalline materials known as of in 1990?s. The study of these solid-state materials has been greatly enhanced by X-ray diffraction techniques. Inside a crystal, a simple geometrical structure of atoms called the basis is repeated in all directions without change in composition, dimension, or orientation. When each basis is replaced by a point, the crystal lattice is obtained. The X-ray diffraction pattern of a crystal, both its geometry and the relative intensity of the spots, gives very valuable information on the lattice structure of the crystal and the composition of the basis. Through this technique, the structure of the crystal can be determined completely, even if it contains some tens or hundreds of thousands of atoms, as in a protein model. As such, the understanding of the diffraction phenomenon has led to the development of a wide variety of scientific disciplines such as physics, chemistry, geology and biology.

The concept of Fresnels zone plate was used by Dennis Gabor in the late 1940?s in his development of the basic principles of holography. As scientific discoveries are continually made, their complete understanding will continue to depend on an understanding of such basic phenomenon as the diffraction of radiation.
Anupam

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7 Oct 2007 09:54:15 IST
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