It should be noted that in the ease shown in the figure, if 0 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. hut two focal lines. It may be that for one particular direction of the incident ray 0 P. these two focal lines. due to two re fractions, cross at a point and thus give prac tically a point for the virtual source. This direction is such that the incident and emerging rays. 0 P and Q II, make equal angles with their respective faces of the prism. For this ray, too, it ma be shown that the deviation is less than for all the other rays from the source 0; and the angle of incidence ur emergence is called the 'angle of minimum deviation.' A prism offers one of the simplest and best n ethods for the measurement of the index of reliactiiin with reference to air of a given ma for definite colors. It may he proved that if A is the angle between the two faces of the prism and I) the angle of minimum deviation for roux of a definite color—both measurable quanti ties—the index of refraction of the material of the prism fur this color is given by the formula A D sin , 71 = sin ,, it is found for all ordinary transparent bodies such as different kinds of glass. water, etc., that
as the color is changed from red to yellow, to green. to hlue, etc., the index of refraction in creases, but at different rates for ditTerent bodies. ln some bodies this is not en; they are said to ex hibit 'anonialou.s' disper sion.
sphrrica/ Surf aces.— Let P .11 he the section of the spherical surface arating two transparent media; let C be the tre of this sphere; t) be the source of a trie pencil, of which 1) P is one ray. and for which n is the index of fraction; let C P Q be a perpendicular to the surface at P and Pit be the refracted ray, Nvlio;e prolongation backward is P 0'. -ks before sill and by geometry it may he shown sin a, = that O' is the virtual image of 0, where 0' lies on the line 0 C which passes through the centre of the spherical surface. and the distance 0' LN1 is such that 1 n. —1 =