LIGHT. 242 LIGHT. it. may be shown that the deviation is less than for all the other rays tidiii the source () ; and the angle of incidence or emergence is called the 'angle of uiiniimiin deviation.' A prism oilers one of the simplest and best methods for the measurement of the index of refraction with reference to air of a given ma- terial for definite colors. It may be proved that if A is the angle between the two faces of the prism and D the angle of minimum deviation for ravs of a definite color — both measurable (pianti- ties — the index of refraction of the material of the prism for tliis color is given by the formula . A + D sin — s— sm A. 9 FlQ. 0. It is found for all ordinary transparent bodies such as dift'erent kinds of glass, water, etc., that as the color is changed from red to yellow, to green, to blue, etc., the inilex of refraction in- crea-ses, but at dilferent rates for diH'erent bodies. In some Ixidies tliis is not so; they are said to ex- hibit 'anomalous' disper- sion. Hphcricnl Surfaces. — IjOt V M be the section of tile spherical surface sep- arating two transparent media ; let C be the cen- tre of this sphere; O be the source of a homocen- tric pencil, of which (> P is one ray, and for which n is the index of re- fraction; let CPQ be a perpendicular to the surface at P and PR be the refracted r.ay, whose prolongation backward is P O', As before -; ^ n, and bv geometry it may be shown Bin aj ' - '^ that O' is the virtual image of O, where 0' lies on the line O C M which passes through the centre of the spherical surface, and the distance O' Jl is such that n 1_ n — 1 (VM =" OM + "CiT LexsBS. a portion of transparent matter bounded by two spherical surfaces and sym- metrical about the line joining their centres is called a 'lens;' this line of symmetry is called the 'axis.' A homncentric jK-ncil of homogeneous rays from any point on the axis gives rise .nfter two refractions to another homocentric pencil with its vertex on the axis. If the source of rays is 0, at a distance u from a thin lens, the image O' will be at a distance y on the opposite side of the lens, where u and i/ are connected by the relation 1 + Ul f being a constant depending on the radii of the two surfaces of the lens and its index of refrac- tion for the particular rays. and 0' are 'con- jugate foci.' If 0' is the real image of O, then will be the image of 0' as a source of rays. (If in this formula, on substituting for « and f their values, v is a negative quantity, 0' is on the same side of the lens as O. ) There are two classes of lenses: for one, f is positive; and for the other, / is negative. (1) /'is essentially positive. — As a special <;ise let O be at an infinite distance, i.e. k = x .ami all the rays from O are lines parallel to the axis. Therefore v = /, a positive quant ity ; and O' is on the opposite side of the lens at a distance f. This point is called the 'principal focus' on that side; and all rays on the other side parallel to the axis pass through this focus after refraction through the lens; for this reason a lens of tliis kind is called a 'ccmverging' one. Similarly, if «=/. r = ao ; i.e. all rays passing through a point on the axis at a distance / from the lens emerge ou the other side of the lens parallel to the axis. There are tlius two principal foci at equa.1 distances from the lens on its two sides. Again, any ray through the jioint where the axis cuts the lens has its dircetitm imaltcred. bi- eause at this point, which is called the 'centre' of the lens, the two surfaces of the lens an' parallel and close together, assuming that the lens is thin. These principles enable one to trace at least three ra.vs leaving a point, and thus to find its image and to draw images for any point or for any object as formed l).v siuh a lens. Drawings are given for a few special cases; It is evident from the formula that if u < f, V <^0 and the image is virtual as shown in Fig. 8. In this case the image is magnified. The plane perpendicular to the axis at a principal focus is called a 'focal plane.' If an object lies in this plane, as shown in Kig. 9, the image of each of its points lies off at infinity, as ap- pears from the fact that the rays are parallel after leaving the lens. Conversely, parallel rays falling upon a lens for which f is positive con- verge after passing through the lens to that point in the focal plane through which passes that one of the piuallel rays which cuts the lens at its middle point or centre. (2) f is essentiallv negative. — As a special ease let O he at an infinite distance, i.e. u = oo and all the rays from are lines parallel to the axis.
