Open AccessThe dispersion of a light pulse by a prism
Author(s) -
R. A. Houstoun
Publication year - 1914
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1914.0052
Subject(s) - prism , pulse (music) , optics , physics , plane (geometry) , dispersion (optics) , expression (computer science) , rest (music) , telescope , mathematics , geometry , computer science , acoustics , detector , programming language
This investigation is a continuation of a former one in which an expression was derived for a light pulse with an energy distribution given by Wien's law. The first three paragraphs are supplementary to the former paper; the rest of the investigation deals with the passage of the same pulse through a prism and its separation into the different colours in the focal plane of a telescope. The general principles according to which this must take place are, of course, known, but here the actual disturbance at every point in the focal plane is given for the first time as a definite function of the time and as a result it is possible to state how many waves there are in the trains, which the single initial pulse gives rise to in the various parts of the spectrum. §1. My general expression for the initial form of a light pulse was cos (n + ½)θ /(x 2 +h 2 )(2n +1)/4, where tanθ =x/h . I did no notice until after the former paper was communicated, that this expression is 1/Г (n + ½) ∫∞ 0 e -ha cosαx α n -½dα .