Diffraction

“ In this process there comes, however, to our aid a very important physical law, namely, the diffraction of light. A ray of light passing through a round hole or a slit and falling on to a black surface is represented not the same size as the slit, but more or less broadened the more the receiving surface is moved away, and in the middle the brightest light will be, and this gradually fades off into shadow towards the margin. ”

“ The subject generally is a curious one, and has interested me for some time; as experiments exhibit several singular phenomena resulting from the interference and diffraction of rays of light in passing by the outline of a material body. As a matter of fact, I believe I may say, that there is no such thing in nature as a perfectly defined outline; since the diffraction of the rays, in passing it, causes them to be projected upon it more or less, according to the nature of the particular body, and the intensity of the light. ”

“ The trouble is we need one that transmits the visible portion of the spectrum and—boy—that's it, Wright, that's it—spectrum—take a totally reflecting diffraction grating, reflect out all that part of the spectrum that we don't want, take what we do, pass it through a prism to recombine it to white light, then through lenses so we can see as if through a telescope! ”

“ THE phenomena of refraction and dispersion teach us that a body in a state of intensest heat emits not alone powerful thermal rays, but also all possible sorts of light (luminous colors) . Diffraction convinces us that radiation is a wave-motion of an extremely fine, elastic, fluid medium, ether, and at the same time it enables us to compute the wave-length of the single rays. ”

“ All these splendid phenomena are, I believe, produced by diffraction, the vesicles or spherules of water in the case of the cloud acting the part of the sporules in the case of the lycopodium. The coloured fringe which surrounds the Spirit of the Brocken, and the spectra which I have spoken of as surrounding the sun, are also produced by diffraction. By the interference of their rays in the earth's atmosphere the stars can momentarily quench themselves ”

“ In such a case the system of bands is achromatic, and the heterogeneity of the light is no obstacle to the formation of visible bands of high order.
These requirements are very easily met by the use of Lloyd’s mirrors, and of a diffraction grating (see Diffraction) with which to form a spectrum. White light enters the dark room through a slit in the window-shutter, and falls in succession upon a grating and an achromatic lens, so as to form a real diffraction spectrum, or rather a series of such, in the focal plane. ”

“ The limitation of power is introduced as in all optical instruments, by the finiteness of the length of a wave of light which causes the image of an indefinitely narrow slit to spread out over a finite width in the focal plane of the observing telescope. The so-called “diffraction” image of a homogeneously illuminated slit shows a central band limited on either side by a line along which the intensity is zero, and this band is accompanied by a number of fainter images corresponding to the diffraction of a star image in a telescope. ”

“ Dark Field Illumination.—As was seen when discussing the physical theory, the minute details of the object cause diffractions, and can only be examined if the objective can take up at least two consecutive diffraction spectra. These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up ”

“ If the incident rays make an angle θ with the normal (fig. 6) , and the diffracted rays make an angle φ (upon the same side) , the relative retardation from each element of width (a + d) to the next is (a + d) (sinθ + sinφ) ; and this is the quantity which is to be equated to mλ. Thus
The “deviation” is (θ + φ) , and is therefore a minimum when θ = φ, i.e. when the grating is so situated that the angles of incidence and diffraction are equal. ”

“ If we carry our experiments with light down to so fine a point that we reach the dimensions of its waves, it is then found that they are capable of bending round obstacles. If sunlight be allowed to pass through an exceedingly fine slit, and then to fall on a screen of white paper, colored bands appear, called diffraction fringes ”

“ The street-lamps at night, looked at through the meshes of a handkerchief, show diffraction phenomena. The diffraction effects obtained in looking through a bird's feathers are, as shown by Schwerd, very brilliant. The iridescence of certain Alpine clouds is also an effect of diffraction which may be imitated by the spores of Lycopodium. When shaken over a glass plate these spores cause a point of light, looked at through the dusted plate, to be surrounded by coloured circles, which rise to actual splendour when the light becomes intense. Shaken in the air the spores produce the same effect. ”

“ Dynamical Theory of Diffraction.—The explanation of diffraction phenomena given by Fresnel and his followers is independent of special views as to the nature of the aether, at least in its main features; for in the absence of a more complete foundation it is impossible to treat rigorously the mode of action of a solid obstacle such as a screen. ”

“ Reverting to fig. 13, we suppose that a diffracting particle of such fineness is placed at O that the diffracted pencils of the 1st order make an angle w with the axis; the principal maximum of the Fraunhofer diffraction phenomena lies in F′1; and the two diffraction maxima of the 1st order in P′ and P′1, . The waves proceeding from this point are united in the point O′. Suppose that a well corrected objective is employed. The image O′ of the point O is then the interference effect of all waves proceeding from the exit pupil of the objective P1P1′. ”

“ It will be observed that, while the total intensity is proportional to ab, the intensity at the focal point is proportional to a2b2. If the aperture be increased, not only is the total brightness over the focal plane increased with it, but there is also a concentration of the diffraction pattern. ”

“ The electric ray at first falls on the grating at a large angle of incidence. A series of flashes of electric radiation are now produced by manipulating the key, and the angle of incidence gradually decreased till the receiver suddenly responds. The angle of incidence corresponding to the zero angle of diffraction is thus determined. The receiver is then placed at a new position on the focal curve, and the corresponding angle of incidence determined as before. In this way a series of angles of incidence, with their corresponding angles of diffraction, are found for each grating. ”

“ He then proceeds to point out the main features in this comparison, claiming justly a great advantage for the theory of undulations on the two points we have been considering, the phenomena of diffraction and of double refraction. And he adds, with reference to the embarrassment introduced by polarization, that we are not to expect the course of scientific discovery to run smooth and uninterrupted; but that we are to lay our account with partial obscurity and seeming contradiction, which we may hope that time and enlarged research will dissipate. ”

“ Again, if the rays be transmitted in two directions, as with certain crystals, “double refraction” (see Refraction, Double) takes place, and the emergent rays have undergone Polarization. A Shadow is cast by light falling on an opaque object, the complete theory of which involves the phenomenon of Diffraction. ”

“ We must not, indeed, forget, that according to the reasoning which has been employed, the formulas for diffraction are only sufficiently exact when this distance is very considerable, in comparison with the breadth of an undulation, since it is in this case only that we can neglect the rays that are decidedly oblique, and [p442] can suppose all those, which are essentially concerned in the effect, to be nearly of equal intensity. ”

“ However, there is a relation which can be traced out between the clearness of the diffraction fringes and the size and shape of the object viewed. This relation is very complex.
The result of such calculation is that the intensity is greatest at the center, whence it rapidly falls off to zero at the first dark band. It then increases to a second maximum, where it is not more than one-ninth as great as in the center. ”

“ The phenomena of diffraction in general may be observed experimentally by plates of glass ruled with fine lines. Fig. 26 shows the appearance presented by a single candle-flame seen through such 38 a plate, an uncoloured image of the flame occupying the centre, flanked on either side by a row of coloured spectra of the flame, which become dimmer as they recede from the centre. ”

“ IN order to complete the explanation of the conditions necessary for the formation of the fringes, it remains to show why a small luminous point must be employed in experiments on diffraction, and not an object of any considerable dimensions. If we resume the case of the interior fringes of the shadow of [p432] a narrow body, it will be easy to apply similar arguments to other cases of diffraction. ”

“ This conclusion can also be arrived at by a mode of reasoning that is independent of the theory of diffraction.15 If linear differential equations admit a solution of the form (5) with A constant, they can also be satisfied by making A a function of the coordinates, such that, in a wave-front, it changes very little over a distance equal to the wave-length λ, and that it is constant along each line conjugate with the wave-fronts. ”

“ Irrationality of Dispersion.—If we compare the spectrum produced by refraction in a glass prism with that of a diffraction grating, we find not only that the order of colours is reversed, but also that the same colours do not occupy corresponding lengths on the two spectra, the blue and violet being much more extended in the refraction spectrum. The refraction spectra for different media also differ amongst themselves. This shows that the connexion between the refrangibility of light and its wave-length does not obey any simple law, but depends on the nature of the refracting medium. ”

“ To study the phenomena of diffraction it is necessary that our source of light should be a physical point, or a fine line; for when a luminous surface is employed, the waves issuing from different points of the surface obscure and neutralize each other. A point of light of high intensity is obtained by admitting the parallel rays of the sun through an aperture in a window-shutter, and concentrating the beam by a lens of short focus. The small solar image at the focus constitutes a suitable point of light. ”

“ Light going round a corner by instruments adapted to show the result, and to measure the angles at which it is turned, is called the diffraction of light.
I can show you an instrument which will measure the wave lengths of light. Without proving the formula, let me tell it to you. A spirit lamp with salt sprinkled on the wick gives very nearly homogeneous light, that is to say, light all of one wave length, or all of the same period. I have a little grating that I take in my hand. I look through this grating, and see that candle before me. ”

“ The discoveries in relation to the constitution and characteristics of light made during the century have been so numerous that we must confine ourselves to those of major importance. Much might be said about the phenomena of polarization, refraction, diffraction, photography, and the development of the power of lenses, to which the great advance in telescopic and microscopic observation is due. ”

“ The topics treated are light and shadow, the visible spectrum, and the eye, polarization, the invisible spectrum of the ultra-violet and the infra-red, and Röntgen light. Interference and diffraction are barely alluded to, and spectrum analysis and the greater part of the subject of color vision are necessarily omitted. In the appendices to chapters the general method of geometrical optics, anomalous refraction and dispersion, the elastic solid, and the electromagnetic theories of light are briefly explained, and "other kinds of invisible light" are described or mentioned. ”

“ The larger the aperture the smaller are the angles through which it is necessary to deviate from the principal direction in order to bring in specified discrepancies of phase—the more concentrated is the image.
In many cases the subject of examination is a luminous line of uniform intensity, the various points of which are to be treated as independent sources of light. If the image of the line be ξ = 0, the intensity at any point ξ, η of the diffraction pattern may be represented by
the same law as obtains for a luminous point when horizontal directions are alone considered. ”

“ The difficulty of conceiving a physical reality corresponding to it has suggested recourse to an optical rationale. Proctor regarded it as an effect of diffraction; [998] Stanislas [Pg 280] Meunier, of oblique reflection from overlying mist-banks; [999] Flammarion considers it possible that companion-canals might, under special circumstances, be evoked by refraction as a kind of mirage. [1000] But none of these speculations are really admissible, when all the facts are taken into account. ”

“ If it were possible to introduce at every part of the aperture of the grating an arbitrary retardation, all the light might be concentrated in any desired spectrum. By supposing the retardation to vary uniformly and continuously we fall upon the case of an ordinary prism: but there is then no diffraction spectrum in the usual sense. To obtain such it would be necessary that the retardation should gradually alter by a wave-length in passing over any element of the grating, and then fall back to its previous value, thus springing suddenly over a wave-length (Phil. Mag., 1874, 47, p. 193) . ”