Diffraction

DIFFRACTION (from Latin diffractus—broken), the bending of waves around obstacles. Diffraction exists for any waves—light waves, sound waves, waves on the surface of a liquid, etc. It is especially pronounced when the size of the obstacle is comparable to the wavelength, and it manifests as deviations from the straight-line propagation of the wave. Sound waves in air have dimensions of approximately the same order as the objects around us; therefore, the diffraction of sound waves is so familiar that it is usually not noticed. On the contrary, light waves are extremely small compared to ordinary objects, and the diffraction of light requires special observation conditions. Arkadyev obtained a diffraction image of scissors by placing a light source, about 1 mm wide, at a distance of 24 m, and a photographic plate behind the scissors at a distance of 15 meters. According to the laws of geometric optics, straight rays from a small source at such distances should give an impeccable shadow; in reality, however, a complex pattern is obtained, speckled with light and dark bands, which is the result of diffraction. The alternating bands or spots in the diffraction pattern are explained by the interference of the diffracted waves; similarly, the decomposition of white light into a spectrum, always observed during diffraction, is connected with interference. If the size of the diffracting slit is small compared to the wavelength, no bands or spots are obtained; after passing through the slit, light is scattered approximately uniformly in all directions. Therefore, to obtain a sharp diffraction pattern, the slit must not be very large, but also not very small compared to the wavelength. Diffraction phenomena are easily observed by squinting one's eye and looking at a distant source through the eyelashes (eyelashes serve as diffraction screens). Diffraction is observed in optical instruments when viewing sufficiently small objects; for example, in a telescope all stationary stars give diffraction circles surrounded by rings; the same occurs in a microscope and an ultramicroscope when viewing objects lying beyond the so-called resolving power of the instrument. The resolving power of an instrument, for example a microscope, is the smallest distance between two individual points when the latter are still perceived separately. The limit of resolving power is entirely determined by diffraction. Due to diffraction, it is impossible to construct a microscope that would allow the detailed examination of objects significantly smaller than the wavelength of light. More precisely, the limit of resolving power of a microscope under the most perfect working conditions (side illumination) is a = λ / (2n sin α). Here n is the half-angle under which the aperture of the objective is seen from the point of the object, and n is the refractive index. Diffraction is used in so-called diffraction gratings to obtain spectra. In its simplest form, a grating is obtained by diamond-cutting a large number of parallel lines on glass. Each gap between the lines acts as a diffraction slit, and the diffracted light from individual slits interferes, resulting in a series of spectra appearing to the right and left of the central white spot when complex light passes through the grating. These spectra and their colors are arranged in a perfectly regular manner; a certain angle under which the light is viewed corresponds to a specific order of the spectrum and a wavelength. The order of the diffraction spectrum is its number. The central undispersed white spot is called the zero-order spectrum, the first spectrum to the right or left is the first order, and so on. The higher the order of the spectrum, the wider it is and the purer the individual colors are. However, spectra of higher orders overlap each other and are very weak, so they are difficult to use. Unlike prismatic spectra, whose dispersion depends on the type of glass, diffraction spectra are always arranged according to one law and are therefore called normal. Dispersion in the red part of the diffraction grating spectrum is significantly greater than in prismatic spectra. For medical purposes, pocket spectrometers and small spectrographs with a diffraction grating are sometimes built to study spectra in the yellow-red part. For precise physical spectral research, so-called Rowland reflection diffraction gratings, which are applied to the concave surface of a mirror metal, are often used. The concave grating itself collects the rays falling on it and gives a real image of the spectrum. The resolving power of the grating, i.e., the minimum distance between two spectral lines at which the lines in a given spectrum do not yet merge, is determined by the product of the total number of grating lines and the order of the spectrum; in Rowland gratings the number of lines reaches hundreds of thousands at a distance of about 1/λ between them; in such instruments wavelengths can be determined with an accuracy of thousandths of a λ. Gratings of this type are suitable for studying the visible spectrum and the entire ultraviolet spectrum (approximately up to 100 nm) under normal conditions. If one studies spectra at almost grazing incidence of rays on the grating, one can obtain X-ray spectra (at least for soft rays). Under normal conditions, however, a diffraction grating for X-rays is not suitable, its holes are too large compared to the wavelength; therefore, instead of an artificial grating, natural ones, namely crystals, are used. In crystals, atoms or molecules are arranged at the nodes of a perfectly regular spatial lattice at distances of the order of 10^-8 cm, comparable to the wavelength of X-rays. Therefore, to obtain X-ray spectra, one uses their diffraction in crystals. For visible rays, the "holes" of the crystal lattice are too small, and noticeable diffraction cannot be obtained. The exact theory of diffraction, which follows fully from the wave theory of light, is one of the most complex chapters of optics in mathematical terms.