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 k_λ, the absorption coefficient of the glass at wavelength λ, and B_s=B/2, the “semibase” of the prism. The variables occur in the combination k_λB_s.

The transmittance, T_λ, 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, T_{λ, 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 Tables and graphs for determining the amount by which the prism must be withdrawn from the beam in order to achieve maximum transmittance are given, again with k_λB_s as variable. Tables and graphs of T_{λ, max}/T_λ 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.

© 1951 Optical Society of America

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