Many substances are really nearly transparent, but appear opaque because they are not homogeneous, so that the entering light is reflected and refracted many times until it is completely scattered. The most obvious example of this is ground glass, but the same is largely true of paper and white wood. An easy test of whether a substance is opaque in this way or by an inherent opacity to light is to see whether it is of the same colour for reflected and transmitted light. A sheet of red paper looks red whether we look at it or through it at a light, because in both cases what we see is light which has got tangled in the fibres, and at each reflexion has lost a little of the green and blue light by ab sorption, so that only the red emerges on both sides. On the other hand if a substance is truly opaque the colours on the two sides will be quite different. For example the yellow colour of gold is due to the fact that it reflects the yellow light more effectively than other colours and, by a paradox which we shall explain later, this means that it absorbs the yellow more strongly. If then we take a very thin sheet of gold, the yellow light will not penetrate it so easily and transmitted light will be bluish green.
The ancients were acquainted with mirrors and with the burn ing glass, but their theories of optics were rather of the meta physical character so much more congenial than experiment to the Greek temperament. The Pythagoreans believed in an emis sion theory, supposing that the seen object emitted particles which bombarded the eye, but the Platonists complicated the matter by supposing that vision was produced by a triple interaction be tween rays emitted by the sun, the object viewed and the eye itself. Among these speculations we can only distinguish the discovery of one real scientific law, enunciated by Hero of Alexandria who saw that the equality of the angles of incidence and reflection at a mirror could be expressed by saying that the ray took the shortest possible course between object and eye. This law is the first statement of the general "principle of least action," a principle which now dominates not only geometrical optics but also dynamics.
We may omit the other speculations of the Greeks, Romans and Arabs and come to the revival of learning. The earliest develop ments were practical, such as the invention of spectacles and later of the telescope, with which we shall not be concerned here. The first great theoretical discovery was the law of refraction dis covered by Snell in 1621, but not published until after his death by Descartes. This law asserts that when a ray of light passes from one medium to another, the plane of the two rays contains the normal to the surface, and the sines of the angles of incidence and refraction are in a constant ratio, the refractive index. Des cartes was led by a metaphysical argument to maintain that light was some sort of pressure in a medium (in a very indefinite way something like the present wave theory), and thought that the velocity of light must be greater in a denser medium. This view
was combated by Fermat, also on metaphysical grounds, and modern theory supports Fermat though not his reasoning. It seems to be the rule rather than the exception that correct results are first obtained from quite incorrect arguments. Fermat asserted that nature performs its operations always by the most direct path, and that therefore a ray of light between two places must take the shortest possible time. The rectilinear propagation of to mean only that which is seen, but it is customary to include in the term various types of invisible radiation, because, though they cannot be seen, in all other respects their behaviour is simi lar. These are the ultra-violet and infra-red radiations which are adjacent to the visible, and, more remotely, on the side of the ultra-violet, the X-rays or Röntgen rays, 7-rays (see RADIO ACTIVITY) and the extremely penetrating cosmic rays; while on the side of the infra-red we have the electromagnetic vibrations of wireless telegraphy. All these radiations have one property in common, an equal speed of propagation. The most accurate measures of the velocity of light (see VELOCITY OF LIGHT) assign it the value cm. per sec. The distinction be tween the various types of radiation depends on wave-length, and the following list shows roughly their wave-lengths measured in centimetres.
light -and the law of reflection conform to this principle, and therefore refraction must do so too. Snell's law then implies that the velocity of light in a medium is inversely proportional to its refractive index. Fermat's "principle of least time" is the natural extension of that of Hero of Alexandria, and was later erected by Hamilton into a general method of great beauty for dealing with optical systems.