Page:The New International Encyclopædia 1st ed. v. 12.djvu/267

LIGHT. 241 LIGHT. Aleohol, 1.36 Glass, soft. 1..52 produces, as before, two focal lines at right angles to each other. It should he observed, further, that the inde.x of refraction — and hence the direction of the refracted rays and the posi- tion.s of the foci — differs for different cidors of the light. Light of a definite index of refraction is called liglit of a "pure' color or "honiogoneous' light. The indices of refraction with reference to air and for the mean wave-length of white light are given for a few substances in the fol- lowing fable: Ulass, hard, 1.60 Water, 1.34 Several special cases of re- fraction will be considered. Phitif Surface. — I^et P II be the section of the plane surface by the paper which is perpen- dicular to it; let O be a point- source of homogeneous light forming a homocentric pencil, of which OP is one of the rays and O JI is the axis ; let P Q be the refracted ray ; S P T be perpendicular to the surface at P; 0' be the inter- section of the line JI with the jjrolongation backward of the refracted rav. Call the angles SPO and fPQ,a, and a, re- spectively. By the laws of refrac- tion '^'" °' is a constant, call it n; then by siu a- ordinary geometry it can be proved that 0' M = j( O il. O' is therefore independent of the direc- tion of the incident ray O P and is the vertex of the refracted homocentric pencil, being a vir- tual image of 0. The diagram is drawn for a case where n < 1, e.g. rays emerging into the air from a bright point below the surface of water. If rays emerging from a bright point in air were entering water, ii > 1 and CK is farther from the surface than O. If light of a different color had been used, i.e. of a different value for n, 0' would have had a different position on the line M. Thus if light of different colors is emitted from O. there will be a series of colored images along Oil. This fact that rays of dif- ferent colors have different images is said to be due to 'chromatic aberration.' Experiments show that in the case of air and glass, or air and water, blue light is refracted more than green, green more than yellow, yellow more than red. A pencil of rays incident obliquely on the plane surface is astigmatic and has two virtual focal lines. If in the above diagram the incident ray OP is so oblique that the refracted ray P Q just grazes the surfaces, a, = 00°. and therefore sin o- = 1. Hence sin o, = n, or a, = sin-'H. If then there should be a ray more oblique than this value of o,. it would be totally reflected, and there wouhl be no refracted ray. This limiting value of the angle of incidence — sin'd — beyond which all rays are totally reflected is called the critical anifle for the two given media separated by the surface and for the particular kind of light for which the index of refraction is n. Plate. — A portion of transparent matter bounded by two plane parallel faces forms a 'plate.' A ray in passing through it from the medium on one side out into the same medium on the other side does not have its direction changed although the emerging ray is displaced sidewise. Prism. — A portion of transparent matter part of whose bounding surface is two plane faces oblique to each other forms a 'prism.' The line in which these two planes meet (or would meet if prolonged) is called the edge of the prism. 9.— -u Fig. 5. Let the paper make a section of the prism per- pendicular to its edge, as in the figxire. Let the index of refraction of the material of the prism with reference to the surrounding medium be greater than 1, then the path of an incident ray O P will be as shown O P— P Q— Q R, the angles of refraction being such as to satisfy the laws of refraction. The direction of the incident ray is P V ; that of the emerging ray. V V Q R ; so the change in direction, or the 'deviation,' is the angle P V W. This deviation is a function of the index of refraction and therefore of the color of the light : so if there are two incident rays of different color along P they will have dif- ferent deviations and on emerging from the prism will be "dispersed.' It should be noted, however, that prisms of different material, e.g. different kinds of glass, disperse the same colors to dif- ferent amounts; this is called 'irrationality' of dispersion ; and it is owing to this fact that 'achromatic' lenses and prisms .are possible. (See Achromatism.) This phenomenon of dispersion may be expressed differently. If is the source of a pencil of rays, it will have a virtual image owing to refraction at the first surface of the prism; the rays diverging from this image will have a virtual image owing to their refraction at the second surface ; so the emerging rays will seem to come from a virtual source on the same side of the prism as O. the actual source. The position of this virtual source varies with the index of refraction of the rays; and different colors will have different virtual sources. So, if O is a source of rays of different colors, there will be a series of virtual sources, one for each color. If the prism is glass and the siirrounding medium air, the virtual image of blue light will be closer to the edge of the prism than that of green light, and this is closer than that of red, referring to Fig. ,5. This shows that the index of refraction n for glass with reference to air is greater for blue than for green, and the in- dex for green is greater than the one for red. It should be noted that in the case shown in the figure, if O P is the central ray of a cone of rays, they form an astigmatic pen- cil ; and so the virtual source is not really a point, but two focal lines. It may be proved that for one particular direction of the incident rav O P, these two focal lines, due to two re- fractions, cross at a point and thus give prac- ticallv a point for the virtiial source. This direction is such that the incident and emerging ravs, O P and Q R, make equal angles with their respective faces of the prism. For this ray, too,