• Y V Kathavate

Articles written in Proceedings – Section A

• Geometric theory of Fresnel diffraction patterns - Part I. Basic ideas

The paper deals with a new approach to the subject of diffraction which enables the nature of the Fresnel pattern due to an obstacle or aperture of arbitrary form to be easily derived. Taking the hint suggested by observation, it is assumed that in the region of shadow the pattern is produced by the interference of radiations having their origin in the boundary of the aperture or the obstacle. In the region of light, the boundary radiation interferes with the primary incident waves and produces the fluctuations of intensity. The radiation from the boundary can again be effectively replaced by spherical waves originating from a finite number of point-sources on the boundary, called ‘poles’, at which the path to the point of observation from the boundary is a maximum or a minimum. This immediately gives a geometric definition of the poles as those points on the boundary whose projection on the plane of observation are the feet of the normals from the observation point to the projection of the boundary. Using this result, it is possible to geometrically map out the positions of maximum and minimum intensity in the diffraction pattern of an arbitrary aperture or obstacle. The relation between the Fresnel and Fraunhofer patterns of an aperture is discussed and it is shown that the Fresnel pattern approaches more and more to the other type as the size of the aperture is diminished or the distance to the observation screen is increased.

• Geometric theory of Fresnel diffraction patterns - Part II. Rectilinear boundaries

In this paper, the Fresnel diffraction patterns of apertures and obstacles having rectilinear boundaries are discussed. Photographs of the patterns in a number of cases such as a square and an equilateral triangle are reproduced. These are explained in terms of the ideas developed in the first paper of this series. The transition from the Fresnel to the Fraunhofer class with square and equilateral triangular apertures is illustrated by means of photographs taken with apertures of decreasing size.

• Geometric theory of Fresnel diffraction patterns - Part III. Boundaries having the shapes of the semi-circle and the segment of a circle

In this paper, the Fresnel diffraction patterns exhibited by apertures and obstacles having the shapes of the semicircle and the segments of a circle are described and explained in terms of the general theory proposed in the first paper of these series. The transition for a semi-circular aperture from the Fresnel to the Fraunhofer class of phenomena as the size of the aperture is diminished is also illustrated.

• Geometric theory of Fresnel diffraction patterns - Part IV. Sectored discs and apertures

Photographs of the Fresnel diffraction patterns exhibited by sectors of a circle are reproduced and are explained on the basis of the general theory developed in an earlier paper. The transition from the Fresnel to the Fraunhofer class as the size of the aperture is diminished is also illustrated with an aperture having the shape of the quadrant of a circle.

• Geometric theory of Fresnel diffraction patterns - Part V. Elliptic obstacles and apertures

Photographs of the Fresnel diffraction patterns of elliptic apertures and obstacles are reproduced. These show many new features hitherto unobserved. For instance, with elliptic dises, a number of bright and dark fringes parallel to the sides of the evolute are found inside it. Another interesting feature is the existence of quasi-elliptic rings outside the evolute, with their longer axis along the minor axis of the geometric shadow. These are found with elliptic apertures also, which besides exhibit bands parallel to the boundary of the ellipse and a fine criss-cross pattern inside the evolute. The patterns are explained in terms of the general theory proposed in Paper I. The transition from the Fresnel to the Fraunhofer pattern as the size of the aperture is diminished is also illustrated.

• Geometric theory of Fresnel diffraction patterns - Part VI. Circular obstacles and apertures

The explanation given by Raman and Krishnan for the difference in the intensities of the central bright spots given by a sphere and a disc of the same diameter has been verified by using four such pairs of different sizes. The Fresnel diffraction pattern of a circular aperture in the region of shadow has been photographed and the transition of this to the Fraunhofer pattern as the size of the aperture is diminished is illustrated.

• The diffraction of light by an assembly of opaque circular disks

The Fraunhofer diffraction pattern of an assembly of artificially prepared small opaque circular disks of identical size is investigated experimentally. It is found that as the distribution of the disks is altered the diffraction pattern undergoes a series of interesting changes. These changes are discussed with reference to the corresponding distributions. Striking optical analogies are presented to various well-known X-ray and electron diffraction effects. Twelve photographs of the diffraction patterns taken in monochromatic light and six in white light are reproduced alongside of the corresponding distributions.

• # Proceedings – Section A

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