The Transmittance of a Prism

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Abstract
The transmittance of a prism for a circular collimated beam of light tangent to the refracting edge of the prism is derived analytically in terms of the first-order modified bessel function of the first kind. The variables involved in the formula are kλ, the absorption coefficient of the glass at wavelength λ, and B8=B/2, the “semibase” of the prism. The variables occur in the combination kλBs.The transmittance, Tλ, computed for a circular beam of diameter d differs little from that computed for a square beam of size d×d.The problem of placing a circular collimated beam on the prism so as to obtain the maximum transmittance, Tλ, max, is reexamined following Hartmann’s treatment. Tables and graphs for determining the amount by which the prism must be withdrawn from the beam in order to achieve maximum transmittance are given, again with kλBs as variable. Tables and graphs of Tλ, max/Tλ are also given.As in the case of square or rectangular beams, the circular-beam transmittance of a combination of several prisms of a given material is found to be identical with that of a single prism of the same material, provided the train of prisms and the single prism give the same angular dispersion.

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