III. On the magnifying-power of the half-prism as a means of obtaining great dispersion, and on the general theory of the 'half-prism spectroscope.'

Abstract

On account of the oblique incidence of the rays on the isosceles prism and the consequent diminution of the aperture of the collimator, a “ half-prism,” formed by dividing an isosceles prism by a plane perpendicular to the base, has frequently been employed for the commencement of the train of prisms, and also for the end, though apparently, without due consideration of the effect of the “half-prism” on the dispersion of the other prisms preceding in the train. This is a matter of some importance; for it will be found that when the angles of incidence and emergence are unequal (as in the half-prism), the angular separation between two pencils of parallel rays is increased or diminished according as the angle of emergence is greater or less than the angle of incidence. In consequence of this the angle between the pencils corresponding to any two lines in the spectrum, e. g . the two D lines, will be increased by passing through a half-prism (independently of the effect of ordinary dispersion) if the perpendicular face be turned towards the slit. At the same time the angle between the pencils coming from the two edges of the slit will, for any monochromatic light, also be increased in nearly the same ratio, and thus the lines in any spectrum become broader as they are further separated by virtue of this property, and the purity of the spectrum remains unaltered. In fact the half-prism is from this point of view equivalent to a cylindrical magnifier, a property which may prove most useful in the construction of the spectroscope, leading to the substitution of three or, at the most, four half-prisms for the long train of fifteen or twenty isosceles prisms now used. For this purpose direct-vision prisms will be most suitable; but I propose to begin by considering the simpler case of a half-prism of flint. The expression“ Magnifying-power” may be conveniently extended to the property in question, which, as will be seen presently, is strictly analogous to that of a lens; for it will be found that the same law holds with combinations of prisms as with other optical combinations, viz. the magnifying-power is the ratio of the breadth of the incident to the breadth of the emergent pencil. In consequence of the property of the half-prism stated above, it becomes necessary to distinguish between separation accompanied by increased breadth of the lines and separation in terms of this breadth. If the sense of the term “dispersion” had not been fixed by usage, it might very well be applied to the latter effect, retaining “separation” for the other; but it will undoubtedly be more in conformity with received ideas to define “dispersion” as the angular length of the spectrum, whilst the term “purity” may be used for the ratio of this angular length to the angular breadth of the spectrum lines (expressed in terms of the angular width of the slit). In the case of an isosceles prism, for which the magnifying-power is 1, the dispersion and purity are equal.