Abstract
IN a little mathematical note in the Comptes rendus M. Thollon investigates the general equation for the passage of light through a prism, and thence deduces the proposition that for every prism there is an angle of minimum resolving power. Differentiating the general equation with respect to the index of refraction, he obtains, first, a differential equation expressing the dependence of the angular distance between two rays upon the dispersive index. A separate differentiation with respect to the angle of incidence yields a second differential equation expressing the dependence of the apparent width of the slit as seen through the prism upon the angular aperture of the slit, as viewed from the prism through the collimator. Hence a relation can be obtained between the angular distance between two rays and their apparent breadth. Further examination of the equations shows that for a certain incidence there will be a minimum of resolution (i.e. an incidence at which the rays are least well defined), and that for another incidence there will be a minimum of dispersion; these two incidences being symmetrically related to the angle of incidence corresponding to minimum deviation. M. Thollon states that these deductions may be readily verified by the following experiment:—A dense flint glass prism is adjusted in the position of minimum deviation for the rays D upon its supporting table in the spectroscope, lit by a sodium flame. The slit is then narrowed or widened until the two yellow rays are just in mutual contact. On then turning the prism around its axis so as to increase the angle of incidence the two rays are seen to separate and to become perfectly distinct, the angular distance between them diminishing all the while. But if the prism be turned in the opposite direction, so as to decrease the angle of incidence, the yellow band is seen to become wider, but without being resolved into two rays. Perhaps this research may explain why the so-called “half prism” spectroscope failed to realise all the hopes of its inventor.
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Physical Notes . Nature 23, 397–398 (1881). https://doi.org/10.1038/023397a0
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DOI: https://doi.org/10.1038/023397a0