. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. DOUBLE REFRACTION. IGl axis as tlie greatest index of refraction is to the least. In the plane of inci- dence lay down the path of the ordinary ray according to the law of Snellius. Through the intersection of this path with the surface of the sphere pass a plane tangent to the sphere; and through the intersection of this tangent plane with the plane of the refracting surface pass another plane tangent to the spheroid. The radius of the sph
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. DOUBLE REFRACTION. IGl axis as tlie greatest index of refraction is to the least. In the plane of inci- dence lay down the path of the ordinary ray according to the law of Snellius. Through the intersection of this path with the surface of the sphere pass a plane tangent to the sphere; and through the intersection of this tangent plane with the plane of the refracting surface pass another plane tangent to the spheroid. The radius of the spheroid drawn to the point of contact Avill be the path of the extraordinary ray. The following is the construction usually given in this case. It has the advantage of involving only the angle of incidence. Let the velocity before refraction be represented by unity; and after refraction let the velocity of the ordinary ray be v, and that of the extraordinary ray perpendicular to the optic axis be i''. With the point of incidence as a centre let there be described a sphere and a spheroid, as before, the radius of the sphere being = r, and the revolving axis of the spheroid being =«/. On the plane of the refracting sur- face and in the plane of incidence take a distance (in the direction of progress) equal to the cosecant of the angle of incidence, and through the point so de- termined draw a perpendicular to the plane of incidence. The plane passing through this perpendicular and touching the spheroid, determines the direction of the extraordinary ray, which, as before, coincides with the radius to the point of contact. To illustrate by a comparatively simple case. In figure 34, let MN be the surfiice of the crystal, and CD the direction of the optic axis. Let also the plane of incidence (represented by the plane of the figure) be a principal section. EC being the direction of the ray and C the point of incidence, make RC = unity, draw CG perpendicidar to RC, and RGr par- allel t
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