Refracting Powers of Bodies. 575 called the angle of refraction, eco. If the degrees of obliquity of the incident and refracted rays from the normal or perpendicular line, a cb, be estimated by the perpendicular distances, da and eo, of points d and e, equally distant from c, it is found that the directions of the original and bent rays so estimated, always bear some invariable relation to each other for the same media. This constant relation is termed the index of refraction. 805. Thus when light passes obliquely from air into water, the line, a d, measuring the obliquity before refraction, is always longer than the line, o e, measuring it after refraction, as the number four to three, and the refraction index of water is therefore said to be . Common glass has the greater refraction index 2, and so on, for other substances. It is important to remark, that for the same substances the same relation always holds, whatever the obliquity of the incidence may be. The following table shows the refractive powers of some well-known solids and liquids, the light being supposed to pass from atmospheric air. From this it will be seen that the diamond occupies the highest As a general rule, the refractive powers of transparent media increase with their densities. It increases, for instance, through this list-air, water, salt, and glass. Newton, while engaged in his experiments upon this subject, observed that combustible bodies had a greater refractive power than corresponds to their density, and he then with singular sagacity hazarded the conjecture, which chemistry has since remarkably verified, that diamond and water both contained combustible ingredients. We now know that diamond is merely crystallized carbon, and that water is composed of hydrogen, an inflammable gas, and oxygen. Diamond has the greatest iight-bending power of any known substances, and to this it owes in part its sparkling brilliancy as a jewel. In consequence of this high refracting power of the diamond, the total reflection of light commences at small angles of incidence, a property which adds greatly to its lustre. Melted phosphorus, naphtha, and sulphide of carbon have a high 576 Effects of Refraction. refracting power on light. The latter is the most refractive liquid known. These are all very inflammable substances. In the lastmentioned liquid, carbon is liquefied in its combination with sulphur. Two combustible substances are here associated, and the refracting power on light is proportionally greater. Its dispersive power is also great. It shares these properties in common with the diamond, and in fact it may be looked upon as liquid diamond. 806. The old explanation, which may be retained to aid popular conception of this phenomenon, was that it is due to an attraction between the light and the refracting denser medium. The light approaching from d to c, for instance (fig. 186), behaves as if attracted by the solid body below it, and is bent into the direction, ce; and, again, on leaving the body, as if equally attracted and bent back again, it takes the direction, ef, instead of en; the attraction and bending being greater, the greater the obliquity. The following are familiar examples of this bending of light in passing from one medium to another : If an empty vessel, bcfe (fig. 187), be in the sun's light, so that the rays falling within it may reach low on the side, as from a to d, but ત b Fig. 187. not to the bottom, then, on filling the J vessel with water, the sun will be found to be shining on the bottom or down to e, as a well as on the side. The reason of this phenomenon is, that water being a denser and more refracting medium than air, the light, on entering it at c, is bent towards the perpendicular (cf), at the point of incidence, and reaches the bottom. So again, if a coin or pebble were laid on the bottom of such a vessel at e, it would not, while the vessel was empty, be seen by an eye at a, but would be visible there immediately on the vessel being filled with water; for then the light leaving the coin in the direction of e c, towards the edge of the vessel, would, at c, on passing from the water into air, be bent away from the perpendicular, and instead of going to g, would reach the eye at a. The coin, moreover, would appear to the eye to be in the direction, cd, higher up, instead of in the true direction, ce, low down: for the eye not being able to discover that the light had been bent in its course, would judge the object to be in the line by which the light arrived. 807. It is thus that objects at the bottom of water, when viewed Illustrations of Refraction. 577 obliquely, do not appear so low as they really are, and that a person viewing the bottom of a river or pond, or any clear water from its bank, naturally judges its depth to be much less than it really is. A person, if looking from a boat directly down upon objects at the bottom, sees them in their true directions, but even then not quite at their true distances, as will be afterwards explained; but if he view them more and more obliquely, the appearance becomes more and more deceptive, until at last it may represent them as being at even less than half of their true depth. An incident witnessed by the writer may be mentioned in illustration. In crossing the Chinese Sea, where no danger was apprehended, an alarm was suddenly given that the ship was among rocks. Through water singularly clear, coral rocks were visible all around and at no great distance; some of them seemed to approach the surface of the water. The sails were instantly backed and soundings were taken, which proved the depth to be greater than appeared. On account of this bending of light from objects under water, there is more difficulty in hitting them with a bullet or spear. The aim by a person not directly over a fish, must be made towards a point apparently below it, otherwise the weapon will miss by flying too high. The spear sometimes used in this country for killing salmon, is a weapon employed among the islanders of the Southern Ocean for killing the albacore. The bending of light, when passing obliquely from water, explains the following facts. A straight rod or stick, of which a portion is immersed obliquely in water, appears crooked at the surface of the water, the portion immersed seeming to be bent upwards. That part of a ship or boat visible under water appears much flatter or not so deep as it really is. A deep bodied fish seen near the surface of water, appears almost a flat fish. A round body there appears oval. To see bodies under water, in their true directions and nearly of their true proportions, the eye must view them through a tube, of which the lower end, closed with plate-glass, is held in the water or through the upright sides of containing vessels formed of plate-glass, now common in aquariums. 808. Gases have, like solids and liquids, a power of refracting light, and, as with solids, those which are most inflammable or combustible possess this power in the highest degree. Hydrogen has the highest, and oxygen the lowest refracting power, the numbers indicative of this being respectively 6614 ar d 861, air being taken at 1000, 578 Atmospheric Refraction. Each compound gas has its own definite power of refracting light, but mixtures of gases have a power depending on the proportions of their ingredients. Thus the refracting power of air, taken at 1000, corresponds to that of a mixture of four parts of nitrogen with one of oxygen. * *A As light is refracted on passing obliquely from air into water, glass, or any other substance denser than air, so also is it bent on coming from empty space into the ocean of our atmosphere. Hence none of the heavenly bodies, except when directly over our heads, are seen by us in their true situations. They all appear a little higher than they really are, and the more so the nearer they are to the horizon. To a spectator at d (fig. 188), supposed to be on the surface of the earth, a star really at A apbpears to be at a, because its OB rays, on reaching the atmosphere at c, are bent downwards. In astronomical books there is always given a table of refractions, showing what correction must be made on Fig. 188. this account for different apparent altitudes. Thus our atmosphere bends the rays of the sun so that we see him in the morning a little while before he is really above the horizon, and we see him in the evening a little while after he is really below it, and thus lengthens the day; for the rays coming horizontally from e to d appear to come from b, although in truth it comes from the lower situation, B, and is bent into the level line only at e. As the atmosphere is denser near the surface of the earth than higher up, the light is more and more bent as it descends, and hence it describes a course which is gently curved, and therefore unlike the course of light in incompressible water. 809. Certain states of the atmosphere, depending chiefly on its humidity and warmth, change very considerably its ordinary refractive power; hence, in one state a distant hill or island may be just visible over an intervening eminence of land, and in other states, the same object will be seen high above, or it may have disappeared altogether. An interesting phenomenon, due to refraction, is often observable in a day of warm sunshine. Black or dark-coloured substances, by absorbing much light and heat from the sun's rays, warm the air in contact with them, and make it dilate and rise in the surrounding air, as oil rises in water. The light then from more distant objects, reaching the eye through the rarefied medium, is bent a little; and owing to the heated air rising irregularly under the influence of the wind and other causes, many objects seem to have a tremulous or a dancing motion. The same phenomenon is to be observed at any time, by looking at an object beyond the top of a chimney from which hot air without smoke is rising. This bending of light by the varying states of the atmosphere, renders necessary the frequent repetition of geometrical observations made in the measuring of heights or of base-lines for the construction of maps and charts. 810. Mirage.—It is to a somewhat similar effect that the phenomenon of the Mirage may be assigned; but in this case there is reflection as well as refraction. Travellers in their journeys across the desert have occasionally seen inverted images of palmtrees, rocks, and other objects, as if reflected from a smooth surface of water between them and the objects. They appeared to be within reach of a beautiful lake; but as they approached the spot, the whole vanished. The explanation of this phenomenon is that the strata of air immediately above the heated sandy soil, are greatly expanded and rarer than the strata above them, which, in spite of the law of diffusion (Art. 459), remain denser. Rays of light proceeding from objects in a direction a little above the level of the earth, and nearly parallel to it, meet the heated and rarer strata at a very obtuse angle. They take the course of a curve as the result of gradual refraction, until at length the angle of incidence, which goes on increasing, reaches the point at which refraction is changed into reflection, and the rays meet the eye of the spectator as if proceeding from an object below the level of the earth. This gives to it the appearance as if it was reflected from the surface of water. The annexed engraving (fig. 189) will show how the strata of air in contact with the heated soil produce this change in the direction of the rays of light, and thus cause an optical illusion. Rays from the palm-tree pass directly to the eye of the spectator, A, in the line, P H. The tree is thus seen in its natural position in the dense portion of the atmosphere. The heated strata are represented by the letters C C, in contact with the surface of the earth, B, increasing in density as they ascend. A ray of light proceeding from H begins to undergo refraction at I. This is increased as it passes |