Light

Huygens' other great investigation is connected with double refraction. Cer tain crystals of calcium carbonate, from Iceland, called cal cite or Iceland spar, have the extraordinary property that ob jects viewed through them appear double. To reduce the mat ter to simpler terms it can be expressed thus : a crystal of calcite resembles a cube that has been compressed along one of its diagonals. Suppose that a narrow beam of light is incident on one face perpendicularly. If the crystal were glass the beam would emerge from the opposite face in the same line. Actually two beams emerge, one in the same way as for glass, but the other, in a new line though in a direction parallel to the first (see fig. 2). These are called the ordinary and extraordinary rays. Huygens successfully applied his wave construction to explain them by supposing that two surfaces must be constructed round each point, one a sphere which would give the ordinary ray, but the other a spheroid with its axis of revolution determined by the crystal axis (that is by the shortened diagonal of the cube) for the extraordinary ray. This is illustrated in fig. 3. Round the points C and D we draw, not only a sphere, but also a spheroid, which is such that the two surfaces touch at the points that lie in the direction of the crystal axis (the point K in fig. 3). The envelope of the spheres is the plane EF which shows the path of the ordinary ray, while the plane Gil is the envelope of the spheroids and shows the path of the extraordinary ray. Observe that the latter ray is not perpendicular to the wave front.

Huygens also discovered, though he did not explain, the phe nomenon of polarization. If we rotate our crystal about an axis in the direction of the beam and observe the projections of the two rays on a screen, the ordinary ray will stay fixed, and the extraordinary, which will be equally bright, will rotate round it. But now suppose that we isolate the ordinary ray and pass it in the same way through a second crystal. In general it will give rise to two rays, ordinary and extraordinary, but this time they will usually be of unequal brightness. If the two crystal axes are parallel, the extraordinary ray will be absent altogether, but as the second crystal is turned it will gradually grow in brightness at the expense of the ordinary, until, when the crystal has turned through a right angle, the ordinary ray will be entirely extin guished. Rotation through a further right angle will restore the ordinary ray and destroy the extraordinary. A similar rule applies for the extraordinary ray from the first crystal; it usually gives both types, but only an extraordinary ray when the crystals have their axes parallel. Newton recognised the essential features of the matter in saying that a ray of light may have sides; in fact that this light differs from ordinary light as a thin lath differs from a round stick. The idea of transverse vibrations had not yet been formulated, so that no further advance could be made at this stage.

We may here remark that the Huygens' wave construction ex plains what some may regard as a philosophic difficulty in Fer mat's principle. According to this principle the rays of light between two points A and B adopt that path which takes the shortest time ; and though the only way we have ordinarily of determining a minimum is to try a number of paths and see which is quickest, yet the ray appears to adopt the right course without any alternative trials. The wave construction explains why it does so, for it shows that the wave is, so to speak, all the time trying alternative routes, and is adopt ing the shortest because the waves in other paths cancel out.

In spite of these great ad vances the state of knowledge at the end of the I 7th century was really insufficient to give a deci sion between the two theories, and moreover there was hardly the beginning of a mathematical wave theory as yet, so it is perhaps not surprising that the corpuscular theory of light gained the upper hand. The 18th century was singularly barren in optics and

the only first-class discovery appeared strongly to support this theory. This was the discovery of stellar aberration, by Bradley (see ABERRATION OF LIGHT), which for corpuscles is immediately explained by the idea of relative motion; whereas with waves, though a crude explanation is not hard, the final solution was only obtained in the loth century with the advent of relativity.

The Age of Fresnel.

The second great period of discovery coincided with the beginning of the 19th century. and the first successes fell to Young. He adopted the wave principle of Huy gens, but extended its application. Thus Huygens had only con sidered waves of the form that we should now call pulses, but Young made use of continuous periodic waves, and so was enabled to explain Newton's rings in a manner we shall discuss later. He clearly stated the general principle of superposition, that "when undulations from different origins coincide, either perfectly or very nearly in direction, their joint effect is a combination of the motions belonging to each." This principle is quite general, but Young perceived that interesting results would only follow when the two sources are coherent, that is to say when two beams from the same source are brought to superposition, for only so could the irregularities in the process of emission be the same for both. He therefore set up what has proved to be one of the classical experiments of optical theory.

Two holes are made close together in a screen, and light from a distant point passes through them and illuminates another screen. If the holes are large there will be merely two patches of light on the screen, but when the holes are made smaller dif fraction occurs, so that the rays of light spread and the patches are larger instead of smaller as might be expected at first sight, When the holes are very small the patches will overlap and it is then observed that they are crossed by a number of fine bands, To understand this let us suppose the light to be monochromatic (of a single wave-length) so that the vibrations of the light-wave are in the form of a travelling sine-curve. The source of light is equidistant from the two holes A and B (fig. 4), so that at those points the waves are in the same phase (shown diagrammatically in the figure). On passing through the small hole each beam emerges as a spherical wave. At the central point 0 of the screen the distances to A and B are equal so the phases agree at every moment ; the effect from the two holes will reinforce one another and 0 will be illuminated. Consider however a point P which is half a wave-length nearer to A than B. Here the waves from A and B are at every time in opposite phases (in the diagram when one wave is at the top the other is at the bottom, etc.) and so cancel, with darkness as the result. At the point Q, which is a whole wave-length nearer to A than B, the waves will reinforce each other again, because one wave is exactly a wave-length be hind the other, and there will be light. Proceeding in this way the whole field is seen to be covered by alternate bright and dark bands. In the case of white light there will be a few coloured bands in the middle and the rest will look white; the colours can be worked out in just the same way as with Newton's rings. Young's interference pattern is by no means easy to ob serve, as it requires very careful adjustments on account of the exceedingly short wave-length of visible light. To give an idea of its magnitude, if the holes are I mm. apart and the screen is at a distance of I metre, then for red light the bright bands are a distance o.6 mm. apart.