174 TOTAL REFLECTION. [102. into a less powerfully refracting medium, as when light passes from glass into air, the obliquity of the refracted ray increases as the angle of incidence increases, until at length the refracted ray becomes parallel to the common surface of the two media. Light, which traverses the more refracting medium and becomes incident upon this common surface at an angle more oblique than this, ceases to be refracted; refraction becomes impossible, and the FIG. 75. P B ray is wholly reflected within the medium. The angle of incidence at which this phenomenon first shows itself is termed the angle of total reflection. In fig. 75, let G G represent a plate of glass with paGrallel sides, P L P a perpendicular at the point of incidence. The incident ray, A L, instead of passing to a', would be refracted from the perpendicular P P to L a on emerging into the air; B L would be still more refracted from L b', and the refracted portion Lb would be nearly parallel with the surface of the glass, whilst c L would be incapable of refraction at all, and would be wholly reflected, as to L c. This phenomenon is easily seen by placing the back to the light and holding a glass of water a little above the level of the eye; on looking obliquely up through the water, a spoon, or other object placed in the glass, will appear to be perfectly reflected upon the surface where the liquid and the air meet. The same thing is seen by holding a glass prism horizontally before a window, and turning it slowly round while the observer faces the window; on looking down into the prism, the internal surface of each face in succession, as it becomes undermost, reflects the lightwith the brilliancy of a mirror. 103.] MEASUREMENT OF REFRACTIVE INDICES. 175 The diamond is indebted for much of its brilliancy to this total reflection, because owing to the high refractive index of this gem, total reflection commences at small angles of incidence. (103) Measurement of the Index of Refraction.—The determination of the refractive index of a body is often a valuable guide in estimating its chemical purity. The adulteration of essential oils may thus be often detected with ease, when it would otherwise be difficult to ascertain it. Wollaston contrived a simple means of determining the refractive index of a body in air, dependent upon the measurement of the angle at which total reflection commences. If this angle be measured in a glass prism, we are furnished with the means of determining the refractive index of the prism in air. Say that the angle c L P (fig. 75), at which total reflection of the incident ray commences in the prison, is found to be 39° 10'; the refractive index of the prism in air is calculated by dividing the sine of the angle of refraction by the sine of this angle of incidence but the angle of refraction at which total reflection begins is always 90°; the refractive index therefore is _Sine 900 Sine 39° 10 or 1899=1583. Now cause a drop of any liquid to adhere to the under surface of the prism; provided that the refractive index of the liquid be less than that of the glass, the angle of total reflection will be increased: suppose the prism be moistened with water, the angle of total reflection will now be 57. The water has a higher refractive index than air, consequently, the difference in refractive index between glass and water being less than that between glass and air, the angle of incidence required to produce total reflection is greater. The refractive index of the substance under trial be ascertained by dividing the sine of its angle of total reflection, under these circumstances, by the sine of the same angle for the glass prism. In the case of water the refractive index is Sine 570 30 or 1336. The refractive index of solids with flat surfaces may be determined in the same way, by cementing them to the surface of the prism with some material of higher refracting power than the glass, such as balsam of tolu. may Sine 39° 10/ 0 8434 Wollaston's instrument, fig. 76, gives at once the refractive index sought without any calculation. FIG. 76. On a board, a b, is fixed a flat piece of deal, c d, to which by a hinge at d, is jointed a second piece, d e, 10 inches long, carrying two plane sights, s and s, at its extremities; at e is a second hinge connecting it with ef, which, if the prism employed has, as supposed, a refractive index of 1583, must be 15.83 inches long; at the other extremity of e f, is a third hinge by which fg is connected with it; at i also is a hinge uniting the rod i g, which is half the length of e f, to the middle of e ƒ; and then, since g moves in a semicircle, a line 176 PRISMATIC ANALYSIS. [103. joining e and g would be perpendicular to fg. The piece c d has a cavity in the middle of it, so that, when any substance is applied to the under surface of the rectangular glass prism, P, the prism may continue to rest horizontally on its extremities. When e d has been so elevated that the yellow rays in the fringe of colours, observable where total reflection terminates, are seen through the sights, the point g, by means of a vernier which it carries, shows upon the rule f, g, which is graduated to fractions of an inch, the number of inches and fractions of an inch which, when divided by 10, gives the refractive index sought. The length of the pieces e ƒ and d e, are proportional to the refractive indices of the prism and of air. If the dotted line at P be a perpendicular to the reflecting surface, IP will represent the incident ray. (Phil. Trans. 1802, 365.) Wollaston mentions that genuine oil of cloves had a refractive index of 1535, but that some of inferior quality, which had probably been adulterated, had a refractive index of only 1'498. The following table contains some of the results obtained by Wollaston with this instrument: Refractive Index of Flint Glass Prism, P = 1.583. Professor Clifton and Mr. Sorby have independently devised a method of determining the refractive index of transparent bodies by placing them in the microscope, and measuring their thickness by the amount of movement of the microscope tube necessary to bring, firstly, the top of the fragment, and, secondly, the glass slide on which they stand, into focus; and subsequently observing the motion necessary to bring into focus a mark on the slide which is seen through the crystal. From these data the refractive index can be determined with accuracy; and the method can be employed with great advantage in recognizing small fragments of minerals. (104) Prismatic Analysis.-Upon examining light that has undergone refraction by a prism, it is found that mere change in direction is only one of the phenomena observable. Suppose a beam of light, as represented at s L, fig. 77, be admitted through FIG. 77. X R 105.] NEWTON'S THEORY OF COLOURS. 177 a small slit, s, into a darkened room, and be there received upon a prism, P; if the light, after transmission through the prism, be allowed to fall upon a white screen, v R x, placed at a distance of three or four metres,-instead of a narrow slit of white light, x, corresponding to the aperture, an elongated coloured image of the slit is seen, as at v R, terminated by parallel ends, and exhibiting the hues of the rainbow. This elongation occurs in the plane of the reflected and refracted rays. image is termed the prismatic spectrum. Such a coloured Newton, who first carefully investigated this remarkable fact, distinguished seven different colours, which gradually shade off one into the other-viz., violet, indigo, blue, green, yellow, orange, and red. White light may therefore be regarded as the result of a mixture of rays of different colours, which are unequally acted upon by the prism. Each colour has its own peculiar refrangibility; the red, which deviates the least from its original course, is least refrangible, and the violet the most so; whilst the intermediate colours possess intermediate degrees of refrangibility. Having once been separated by refraction, no second refraction is capable of further decomposing any of these colours. They may, however, be recombined by using a second prism, in an inverted position (as shown by the dotted lines at Q, fig. 77), or by employing, what amounts to the same thing, a convex lens, in which case white light is reproduced at the focus of the lens. The composition of white light may be illustrated by dividing a circular disk of paper into seven sectors, each of an extent corresponding with the extent of the colour in the spectrum, and painting each with its appropriate colour; on causing the disk to rotate rapidly upon an axis passing vertically through its centre, the seven impressions will be given simultaneously to each point of the retina, and the paper will appear to be of a greyish white. The impossibility of obtaining pigments of the exact hue, or of the brilliancy of the coloured light of the spectrum, renders a pure white unattainable by this means. The following is an elegant mode of showing the recomposition of white light from the colours of the spectrum. A prism is mounted so as to permit of a movement on its axis through a small arc, the spectrum is thus made to travel on a screen in the direction of its length. On moving the prism slowly, the colours are visible; but when the prism is made to oscillate very rapidly the colours are blended together, producing a streak of white light with a red border at one end and a blue at the other. (105) Theory of Colours.-Upon this decomposibility of white 178 DECOMPOSITION OF LIGHT BY ABSORPTION. [105. light, Newton founded his explanation of the colours of natural objects :-The objects are themselves devoid of colour, but when placed in white light they absorb the rays of one or more colours, and reflect the rest: the object, therefore, appears to be of the colour that would be produced by the ray or mixture of rays which it reflects; green objects, for example, absorb the red rays and reflect the yellow and the blue; purple absorb the yellow, and reflect the red and the blue. The rays thus absorbed are said to be complementary to those that are reflected; a complementary colour being always that tint which when added to the primary colour upon the eye would constitute white light. This theory of colours may be illustrated by placing any coloured objects in light of one tint, or homogeneous light, as it is calied, such as that of an isolated portion of the spectrum. A purple object, for instance, when placed in the blue rays will appear to be blue: if placed in the red rays it will appear to be red; and a white screen, which has the power of reflecting all the colours, will take any tint in succession, according to the colour of the incident ray. An object of a pure red, on the contrary, will appear to be black in any but the red ray, because it absorbs all the other colours as perfectly as charcoal or black velvet absorbs white light or rays of all colours. Hence it appears that white light may be decomposed by absorption, as well as by refraction or prismatic analysis. By transmitting white light through transparent coloured media, we may obtain rays of any given tint: the light thus obtained is not always the same as that produced by prismatic analysis, though apparently of the same colour; by transmission through a coloured medium, a green, for instance, may be obtained, which may either be identical with the green isolated by the prism, and then it cannot further be separated into its components; or it may be a compound colour resulting from the intermixture of rays of different degrees of refrangibility, and in this case it is susceptible of further decomposition. The coloured light that is obtained by absorption is seldom so pure as that furnished by prismatic decomposition. Gladstone (Q. J. Chem. Soc. 1856, x. 79) has made some interesting observations upon the relation existing between the chemical composition, of a body and the absorbent effect which it exerts upon transmitted light. His experiments were performed upon substances in solution which were placed in a wedge-shaped vessel or hollow prism, with the view of ascertaining the influence of different thicknesses of liquid upon the incident light. A beam of diffused light was admitted through a vertical slit into a darkened chamber, and the line of light thus obtained was allowed to fall upon the vessel held with the thin end of the wedge downwards, so that the light passed through different thicknesses of the solution, from the thinnest filin to a stratum of an inch (25mm) in depth. The transmitted light |