Dr. Feussner gives a mathematical analysis of the paths taken by the two polarized rays within the Nicol prism, and finds that the emergent extraordinary ray can include an angular field of 29°, but that this extreme value holds good only for rays incident upon that portion of the end surface which is near to the obtuse corner, and that from thence it gradually decreases until the field includes an angle of only about half the previous amount. He finds, moreover, that, although of course the ray emerges parallel to its direction of incidence, yet that the zone of polarized light is shifted to one side of the central line. Also that the great length of the Nicol—3.28 times its breadth—is not only an inconvenience, but owing to the large pieces of spar thus required for its construction, prisms of any but small size become very expensive. To this it may be added that there is a considerable loss of light by reflection from the first surface, owing to its inclined position in regard to the long axis of the prism.
Figs. 4., 5., and 6.
It is with the view of obviating these defects that the modifications represented in Figs. 2 to 6 have been devised.
2. The Shortened Nicol Prism.—This arrangement of the Nicol prism is constructed by Dr. Steeg and Reuter of Homburg v.d.H. For the sake of facility of manufacture, the end surfaces are cleavage planes, and the oblique cut, instead of being perpendicular, makes with these an angle of about 84°. By this alteration the prism becomes shorter, and is now only 2.83 times its breadth; but if Canada balsam is still used as the cement, the field will occupy a very unsymmetrical position in regard to the long axis. If balsam of copaiba is made use of, the index of refraction of which is 1.50, a symmetrical field of about 24° will be obtained. A prism of this kind has also been designed by Prof. B. Hasert of Eisenach (Pogg. Ann., cxiii., 189), but its performance appears to be inferior to the above.
3. The Nicol Prism with Perpendicular Ends.—The terminal surfaces in this prism are perpendicular to the long axis, and the sectional cut makes with them an angle of about 75°. The length of the prism is 3.75 times its breadth, and if the cement has an index of refraction of 1.525, the field is symmetrically disposed, and includes an angle of 27°. Prisms of this kind have been manufactured by Dr. Steeg, Mr. C.D. Ahrens, and others.
4. The Foucault Prism (Comptes Rendus, 1857, xlv., 238).—This construction differs from all those hitherto mentioned, in that a film of air is employed between the two cut surfaces as the totally reflecting medium instead of a layer of cement. The two halves of the prism are kept in position, without touching each other, by means of the mounting. The length of the prism is in this way much reduced, and amounts to only 1.528 times its breadth. The end surfaces are cleavage planes, and the sectional cut makes with them an angle of 59°. The field, however, includes not more than about 8°, so that this prism can be used only in the case of nearly parallel rays; and in addition to this the pictures which may be seen through it are to some extent veiled and indistinct, owing to repeated internal reflection.
5. The Hartnack Prism (Ann. de Ch. et de Physique, ser. iv., vii., 181).—This form of prism was devised in 1866 by MM. Hartnack and Prazmowiski; the original memoir is a valuable one; a translation of it, with some additions, has lately been published (Journ. of the R. Microscopical Soc., June, 1883, 428). It is considered by Dr. Feussner to be the most perfect prism capable of being prepared from calc-spar. The ends of the prism are perpendicular to its length; the section carried through it is in a plane perpendicular to the principal axis of the crystal. The cementing medium is linseed oil, the index of refraction of which is 1.485. This form of prism is certainly not so well known in this country as it deserves to be; a very excellent one, supplied to the present writer by Dr. Steeg is of rectangular form throughout, the terminal surfaces are 19 × 15 mm., and the length 41 mm. The lateral shifting of the field is scarcely perceptible, the prism is perfectly colorless and transparent, and its performance is far superior to that of the ordinary Nicol. The field of view afforded by this construction depends upon the cementing substance used, and also upon the inclination of the sectional cut in regard to the end of the prism; it may vary from 20° to 41°. If the utmost extent of field is not required, the prism may be shortened by lessening the angle of the section, at the expense, however, of interfering with the symmetrical disposition of the field.
6. The Glan Prism (Carl's "Repertorium," xvi., 570, and xvii., 195).—This is a modification of the Foucault, and in a similar manner includes a film of air between the sectional surfaces. The end surfaces and also the cut carried through the prism are parallel to the principal axis of the calc-spar. The ends are normal to the length, and the field includes about 8°. This prism is very short, and may indeed be even shorter than it is broad. It is subject to the same defect as that mentioned in the case of the Foucault, although perhaps not quite to the same extent.