REFRACTION. One must distinguish between bonmeentrie and astigmatic pencils in refraction as well as in reflection; for a homocentric pen cil of incident rays produces a homocentric pencil of refracted rays, thus giving a point-focus, either real or virtual; and an astigmatic pencil produces, as before, two focal lines at right angles to each other. It should he observed, further, that the index of refraction—arid the direction of the refracted rays and the posi tions of the foci--differs for different colors of the light. Light of a definite index of refraction is called light of a 'pure' color or 'homogeneous' 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 table: Aleola,l, Las Glass, hard, 1.66 Glass. .oft. 1.52 Water, 1.34 Several special cases of re fraction will be considered.
Plane Surfacc.—Let 1' Al be the section of the plane surface by the paper which is perpen dicular to it; let 0 be a point pource of homogeneous light forming a homocentrie pencil, of which 01' is one of the rays and 01\1 is the axis; let P Q be the refracted ray; S 1' T be perpendicular to the surface at 1'; 0' be the inter section of the line 0 with the prolongation backward of the refracted ray. Call the angles S p 0 and T P Q, a, and re spectively. Bythe laws of refrac tion sin a, is a constant, call it n; then by sin a ordinary geometry it can be proved that 0' Al n () Al. 0' is therefore independent of the direc tion of the incident ray P and is the vertex of the refracted homocentrie pencil, being a vir tual image of O. The diagram is drawn for a case where n < I. 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. n >1 and 0' is farther from the surface than O. If light of a different color had been used, i.e. of a different value for 71, 0' would have had a different position on the line 01\1. Thus if light of different colors is emitted from 0, there will he a series of colored images along 0 This fact that rays of dif ferent eolors have different images is said to be (Inc to 'chromatic aberration.' Experiments show that in the ease 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 ineidcnt ray 0 P is so oblique that the refracted ray P Q just grazes the surfaces, a, = 90°, and therefore sin = 1. Hence sin a, = n, or a, = sin If then there should be a ray more oblique than this value of a,, it W0111(1 be totally reflected, and there would be no refracted ray. This limiting value of the angle of which all rays are totally reflected is called the critical angle for the two given media separated by the surface and for the particular kind of light for which the index of refraction is n.
Platc.—A portion of transparent matter hounded 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 hounding surface is two plane face.. oblique to each other forms a 'prism.' The line in \\lie!' these two planes tweet (or would meet if prolonged) is called the edge of the prism.
Let the paper make a section of the prism per pendicular to its edge, as in the figure. 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 1' will lie as shown 0 Q—Q II, the angles of refraction being such as to satisfy the laws of refraction. The direction of the incident ray is 0 P V; that of the emerging ray. W V Q It; so the change in direction, or the `deriation.' 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 0 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 he expressed differently. if 0 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 0, 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 0 is a source of rays of different colors, there will he a series of virtual sources, one for each color. If the prism is glass and the surrounding 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 des for green is greater than the one for red.