The London, Edinburgh and Dublin philosophical magazine and journal of science . transmitted. Shouldtoo great an inclination be given, the ordinary as well as theextraordinary will be transmitted and the emergent beamwill no longer be plane-polarized. In view of this it seemed desirable to determine from such * Communicated by Prof. L. R. Wilberforce. Polarizing Prisms for the Ultraviolet. 257 data as were available the limiting values of the angles ofinclination of the air-film for transmitting polarized beams ofshort wave-length. The results, as they may be of interestto others working in th
The London, Edinburgh and Dublin philosophical magazine and journal of science . transmitted. Shouldtoo great an inclination be given, the ordinary as well as theextraordinary will be transmitted and the emergent beamwill no longer be plane-polarized. In view of this it seemed desirable to determine from such * Communicated by Prof. L. R. Wilberforce. Polarizing Prisms for the Ultraviolet. 257 data as were available the limiting values of the angles ofinclination of the air-film for transmitting polarized beams ofshort wave-length. The results, as they may be of interestto others working in the same department of optics, are forthree special cases given in the present note. These are,namely :— I. A square-ended Foucault, the end faces being per-pendicular to the line of vision, and to the planes containingthis line and the optic axis. II. An ordinary Foucault, the end faces being the naturalends of the crystal. III. A Glan-Foucault prism. The angles of a natural crystal of spar are indicated infig. 1, which represents a principal section-plane. We shall Fig-.].. denote the inclination of the dividing plane AB to the line ofvision by a or yS according as we are dealing with the extra-ordinary or ordinary ray respectively. Let //,o=the ordinary index of refraction for light of wavelength \ ;/xe = the extraordinary index of refraction for light of wave-length X ;a = the semi-major axis and b = the semi-minor axis ofthe elliptic section of the extraordinary wave-sheet ;r = the radius-vector of the ellipse in the direction of the ray within the crystal ;# = the inclination of r to the major axis in the plane containing the optic axis ;$ = the inclination of the tangent plane (at the pointwhere r meets the ellipsoid) to the major axis. Then, if the velocity of light in air be denoted by unity,we have _ 1 _ 1 # velocity in air _ 1 0— £ a ray velocity along r r Phil. Mag. S. 0. Vol. 28. No. 164. Aug. 1914. S -jD^ Mr. S. S. Richardson on Also, considering only the rays
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