CHAPTER VI.

DIFFRACTION.

(88) IT has been shown to be a result of the wave-theory, that the intensity of the light which encounters an obstacle must diminish rapidly within the edge of the geometric shadow. It now remains to consider the other phenomena which arise under these circumstances; and it will be found that the same theory affords the most complete account, not only of their general characters, but even of their most minute details.

In order to understand the theory of shadows, it is necessary to investigate their laws in the simple case in which the magnitude of the luminous body is reduced to a point. The effects thus presented were first observed, and in some degree explained, by Grimaldi; and they have been since studied, as a separate branch of Optical Science, under the title of diffraction or inflexion.

Grimaldi found, that when a small opaque body was placed in the cone of light, admitted into a dark chamber through a very small aperture, its shadow was much larger than its geometric projection; so that the light suffered some deviation from the rectilinear course in passing by the edge. On observing these shadows more attentively, he found that they were bordered with three iris-coloured fringes, which decreased in breadth and intensity in the order of their distances from the shadow, and which preserved the same distance from the edge throughout its entire extent, unless where the body terminated in a sharp angle. Similar fringes were observed, under favourable circumstances, within the shadows of narrow bodies.

The phenomena of diffraction were subsequently examined by Hooke and by Newton; and, lastly, in the hands of Young and Fresnel, they have been forced to furnish evidence in favour of the wave-theory, which few who impartially examine it can continue to withstand. We shall first describe the most important of these phenomena, and afterwards examine them in their bearing upon the two theories.

(89) The most obvious of these phenomena are the modifications which light undergoes in passing by the edge of an obstacle of any kind.

Let a beam of homogeneous light, entering a dark chamber, fall on a lens of short focal length, MN, by which it is

brought to a focus at O, and thence diverges. Let an obstacle, PP', be placed in the diverging beam, and let the shadow which it casts be received upon a sheet of white paper at Q, or on a piece of roughened glass. We shall then observe the following phenomena :

I. The line OPQ, which is the boundary of the geometric shadow, is not the actual boundary of light and shade.

II. The space below this line, QS, is not absolutely dark, but is enlightened by a faint light, which extends to a sensible distance within the geometric shadow, and gradually fades away as it recedes from the edge of this shadow at Q.

III. On the other side of the boundary of the geometric shadow, at QR, the paper is not uniformly illuminated by the diverging beam, but is observed to be covered with a series

of alternate bright and dark bands, which are parallel to the edge of the shadow. The distances of these fringes inter se, and from the edge of the shadow, vary with the position of the screen, and diminish indefinitely as the screen is brought near the obstacle. These fringes succeed one another for many alternations, becoming, however, less marked as the distance from the edge of the geometric shadow increases, until at length they are wholly obliterated and lost. They preserve the same distances from the shadow in all parts, except only where the edge of the body forms a sharp angle.*

IV. The dimensions of the fringes vary with the colour of the light; being broadest in red light, narrowest in violet light, and of intermediate magnitude in the light of mean refrangibility. Hence, when white or compound light is employed, the fringes of different colours will not be accurately superposed; and there will be formed a succession of iris-coloured fringes, the colours following the order which they have in the spectrum.

(90) If we follow the course of the fringes from their origin, we shall observe that they are propagated in lines sensibly curved, whose concave side is turned towards the shadow. In order to obtain accurate measures of the distances of the fringes from the edge of the shadow, at different distances from the obstacle, Fresnel viewed them directly with an eye-piece, furnished with a micrometer. He thus ascertained that the curved path of each fringe was an hyperbola, whose summit coincided with the edge of the obstacle, and whose centre was the middle point of the line connecting that edge with the luminous origin.

* If this angle be salient, the fringes, instead of forming a similar angle, are observed to curve round the shadow. When the angle is re-entrant, they cross, and enter on the shadow at each side, without interfering with one another.

If we consider these hyperbolas as coincident with their asymptots (which may be done without sensible error, unless near the edge of the obstacle), and if we then determine the angles which they make with one another, and with the edge of the geometric shadow, we shall find that these angles increase rapidly as the distance of the obstacle from the luminous point diminishes. When this distance is about 40 inches, the fringes are very close together, the fringes of the first and second order making an angle with one another of less than 2' in red light. At the distance of 4 inches this angle is increased to more than 5'; and at of an inch it exceeds 16'. Thus the fringes dilate, as the edge of the obstacle approaches the luminous origin.

(91) In this experiment the incident light is supposed to diverge from a luminous point. If the dimensions of the luminous origin had been considerable, it will be easily understood that each line in it, parallel to the edge of the obstacle, would give rise to a different system of fringes; and, as the dark bands of some of these systems must coincide with the bright bands of others, every trace of the phenomenon would be obliterated.

(92) The preceding experiments exhibit the effect of a single edge. When the light diverging from the luminous point is suffered to pass by two near edges, the phenomena will be varied in a very interesting manner.

Let a fine wire be placed in the pencil of light diverging from a luminous point, and let its shadow be received on a screen, or plate of roughened glass, as before. We then observe, outside the geometric shadow, a set of parallel bands, or fringes, analogous to those produced by the single edge in the former experiment. These are the exterior fringes. But we observe further that the whole space of the geometric shadow itself is also occupied by parallel stripes, alternately

bright and dark. These are the interior fringes; and they are in general closer, and more finely marked than the exterior. When the breadth of the obstacle is considerable, the interior fringes disappear, and the phenomena fall under the class already examined.

The interior fringes are propagated, like the exterior, in hyperbolic curves; but their curvature is less considerable, and the deviation from a right-lined course is scarcely perceptible within the limits at which they are commonly observed. They are also, like the exterior fringes, broader in red than in violet light, and of intermediate breadths in the light of intermediate refrangibility. Accordingly, in compound or white light, the fringes of different dimensions are superposed; and the bands are no longer alternately bright and black, but coloured with different tints, in the order of the colours of the spectrum.

(93) It still remains to examine the effects produced by two edges turned inwards, so as to form an aperture of any dimensions.

For this purpose Fresnel employed an instrument consisting of two metallic plates, one of which is fixed in the frame of the apparatus, while the other is moveable by means of a fine The edges of these plates are right-lined and parallel, so that they form always a rectangular aperture; and, by means of the adjusting screw, the magnitude of this aperture may be varied at pleasure.

screw.

When a narrow rectangular aperture, thus formed, is substituted for the wire in the last experiment, the resulting phenomena are very remarkable. In the first place, the luminous beam diverges considerably after passing the aperture, so that the space which it occupies on the screen, or roughened glass, is much wider than the geometric projection of the aperture. Secondly, the entire of this space is covered with parallel bands, or fringes, alternately bright and dark, distributed symmetri