In comparing the various forms of polarizing prisms, the main points
which need attention are--the angular extent of the field of view, the
direction of the emergent polarized ray, whether it is shifted to one
side of, or remains symmetrical to the long axis of the prism; the
proportion which the length of the prism bears to its breadth; and
lastly, the position of the terminal faces, whether perpendicular or
inclined to the long axis. These requirements are fulfilled in
different degrees by the following methods of construction:
[Illustration: Fig. 1., Fig. 2., and Fig. 3.]
1. _The Nicol Prism_ (_Edin. New Phil. Journal_, 1828, vi., 83).--This
(Fig. 1), as is well known, is constructed from a rhombohedron of
Iceland spar, the length of which must be fully three times as great
as the width. The end faces are cut off in such a manner that the
angle of 72° which they originally form with the lateral edge of the
rhombohedron is reduced to 68°. The prism is then cut in two in a
plane perpendicular to the new end surfaces, the section being carried
obliquely from one obtuse corner of the prism to the other, in the
direction of its length. The surfaces of this section, after having
been carefully polished, are cemented together again by means of
Canada balsam. A ray of light, on entering the prism, is separated by
the double refraction of the calc-spar into an ordinary and an
extraordinary ray; the former undergoes total reflection at the layer
of balsam at an incidence which allows the extraordinary ray to be
transmitted; the latter, therefore, passes through unchanged. This
principle of obtaining a single polarized ray by means of total
reflection of the other is common to all the forms of prism now to be
described.
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.
[Illustration: Fig. 4., Fig. 5., and Fig. 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.