=60. Optical Properties of Natural Sugars.=—The solutions of all
natural sugars have the property of deflecting the plane of polarized
light and the degree of deflection corresponds to the quantity of sugar
in solution. By measuring the amplitude of the rotation produced the
percentage of sugar in the solution can be determined. In order to
secure accuracy in the determinations it is necessary that only one
kind of sugar be present, or, if more than one, that the quantities
of all but one be determined by other means, and the disturbances
produced thereby in the total rotation be properly arranged. In point
of fact the process in practice is applied chiefly to cane and milk
sugars, both of which occur in nature in an approximately pure state.
The process is also useful in determining cane sugar when mixed with
other kinds, by reason of the fact that this sugar after hydrolysis
by treatment with a weak acid for a long or a strong acid for a short
time, definitely changes its rotating power. Since, by the same
treatment, the rotating power of other sugars which may be present is
only slightly altered, the total disturbance produced is approximately
due to the inversion of the cane sugar.
Dextrose and maltose arising from the hydrolysis of starch may also
be determined with a fair degree of accuracy by their deportment
with polarized light. When a solution of natural sugars shows
negative results when examined with polarized light, it is due to an
admixture of two or more sugars of opposite polarizing powers in such
proportions as to produce neutrality. This condition often occurs
in the examination of honeys or in submitting artificial sugars to
polarimetric observations. In the latter case the neutrality is caused
by the tendency manifested by artificially produced sugars to form twin
compounds of optically opposite qualities.
The instrument used for measuring the degree of deflection produced in
a plane of polarized light is called a polariscope, polarimeter, or
optical saccharimeter. For a theoretical discussion of the principles
of polarization and the application of these principles in the
construction of polariscopes, the reader is referred to the standard
works on optics and the construction of optical instruments.[35] For
the purposes of this work a description of the instruments commonly
employed and the methods of using them will be sufficient.
=61. Polarized Light.=—When a ray of light has been repeatedly
reflected from bright surfaces or when it passes through certain
crystalline bodies it acquires peculiar properties and is said to be
polarized.
Polarization is therefore a term applied to a phenomenon of light, in
which the vibrations of the ether are supposed to be restricted to a
particular form of an ellipse whose axes remain fixed in direction. If
the ellipse become a straight line it is called plane polarization.
This well-known phenomenon is most easily produced by a nicol prism,
consisting of a cut crystal of calcium carbonate (Iceland spar). This
rhombohedral crystal, the natural ends of which form angles of 71° and
109°, respectively, with the opposite edges of its principal section,
is prepared as follows:
The ends of the crystals are ground until the angles just mentioned
become 68° and 112°. The crystal is then divided diagonally at right
angles with the planes of the ends and with the principal section, and
after the new surfaces are polished they are joined again by canada
balsam. The principal section of this prism passes through the shorter
diagonal of the two rhombic ends. If now a ray of light fall on one
of the ends of this prism, parallel with the edge of its longer side,
it suffers double refraction, and each ray is plane polarized, the
one at right angles with the other. That part of the entering ray of
light which is most refracted is called the ordinary and the other the
extraordinary ray. The refractive index of the film of balsam being
intermediate between those of the rays, permits the total reflection of
the ordinary ray, which, passing to the blackened sides of the prism,
is absorbed. The extraordinary ray passes the film of balsam without
deviation and emerges from the prism in a direction parallel with the
incident ray, having, however, only half of its luminous intensity.
Two such prisms, properly mounted, furnish the essential parts of a
polarizing apparatus. They are called the polarizer and the analyzer,
respectively.
If now the plane of vibration in each prism be regarded as coincident
with its principal section, the following phenomena are observed:
If the prisms are so placed that the principal sections lie in the
prolongation of the same plane, then the extraordinary polarized ray
from the polarizer passes into the analyzer, which practically may
be regarded in this position as a continuation of the same prism.
It happens, therefore, that the extraordinary polarized ray passes
through the analyzer exactly as it did through the polarizer, and is
not reflected by the film of balsam, but emerges from the analyzer
in seemingly the same condition as from the polarizer. If now the
analyzer be rotated 180°, bringing the principal section again in the
same plane, the same phenomenon is observed. But if the rotation be in
either direction only 90°, then the polarized ray from the first prism,
incident on the second, deports itself exactly as the ordinary ray,
and on meeting the film of balsam is totally reflected. The field of
vision, therefore, is perfectly dark.
In all other inclinations of the planes of the principal sections of
the two prisms the ray incident in the analyzer is separated into
two, an ordinary and extraordinary, varying in luminous intensity in
proportion to the square of the cosine of the angle of the two planes.
[Illustration: FIGURE 31. COURSE OF RAYS OF LIGHT IN A NICOL.]
Thus, by gradually turning the analyzer, the field of vision passes
slowly from maximum luminosity to complete obscurity. The expression
crossed nicols refers to the latter condition of the field of vision.
=62. Description of the Prism.=—In a nicol made as described above,
Fig. 31, suppose a ray of light parallel with the longer side of the
prism be incident to the end _a_ _b_ at _m_. By the double refracting
power of the spar the ray is divided into two, which traverse the first
half of the prism. The two rays are polarized at right angles to one
another. The less refracted ray when it strikes the film of Canada
balsam passes through it without interference. The more refracted ray
strikes the balsam at _o_ at such an angle as to be totally reflected
and made to pass out of the prism in the direction _o r_. If the prism
be blackened at the surface the ray will be entirely absorbed. The
other ray passes on through the other half of the prism and emerges in
the direction of _qs_. It is evident that the emergent light from a
nicol has only half the illuminating power possessed by the immergent
rays.
The polarized plane of light from the nicol just described may be
regarded as passing also into a second nicol of essentially the same
construction as the first.
This second nicol, called the analyzer, is so constructed as to
revolve freely about its longitudinal axis, and is attached to a
graduated circle in such a way that the degree of rotation can be
accurately read. If the planes of polarization of the two nicols are
coincident when prolonged, the ray of light passing from the first
nicol will pass through the second practically unchanged in character
or intensity. If, however, the analyzing nicol be turned until the
plane of polarization is at right angles to that of the polarizer the
immergent ray will suffer refraction in such a manner as to be totally
reflected when reaching the film of balsam and will be thus entirely
lost. In making a complete revolution of the analyzer, therefore, two
positions of maximum intensity of light and two of darkness will be
observed. In intermediate positions the ray immergent to the analyzer
will be separated as in the first instance into two rays _g p_ varying
intensities, one of which will be always totally reflected.
[Illustration: FIGURE 32. THEORY OF THE NICOL.]
In Fig. 32 is given a more detailed illustration of the action of the
rays of light. The film of balsam is represented as enlarged and of
the thickness _bb_. Draw the perpendiculars represented by the dotted
lines _n_₁ _n_ʹ₁, _n_₂ _n_ʹ₂, _n_₃ _n_ʹ₃ and _n_₄ _n_ʹ₄. In passing
into the prism at _m_ both refracted rays are bent towards the normal
_m n_ʹ₁. The degree of deflection depends on the refractive index of
the two rays 1.52 and 1.66 respectively. The refractive index of the
extraordinary ray in calcspar being 1.52, and in Canada balsam 1.54,
it suffers but little disturbance in passing from one to the other.
On the other hand the balsam, being considerably less refractive
for the ordinary ray than the calcspar, causes that ray to diverge
outwards from the normal _o n_ʹ₂, and to such a degree as to suffer
total reflection. The critical angle, that is the angle at which a ray
issuing from a more refractive into a less refractive medium, emerges
just parallel to the bounding surfaces, depends on the relative index
of refraction. In the case under consideration the ratio for balsam
and spar is 1.54/1.66 = 0.928 = sin 68°. Therefore the limiting value
of _m o_ _n_₃ so that _m o_ may just emerge in the direction _od_ is
68°. If now _mo_ were parallel to _o d_ the angle _m o n_, would be
just 68°, being opposite _b a d_. which has been ground to 68° in the
construction of the prism. But in passing into the prism, _m o_ is
refracted so that the angle _m o n_₃ is greater than _b a d_. It is
therefore always certain that by grinding _b a d_ to 68° the ordinary
ray _m o_ will be with certainty entirely thrown out in every case. In
respect of the analyzing nicol the following additional observations
will be found useful. In all uniaxial crystals there are two directions
at right angles to each other, one of greatest and one of least
resistance to the propagation of luminous vibrations. These planes are
in the direction of the principal axis and at right angles thereto.
Only light vibrating in these two directions can be transmitted through
calcspar; and all incident light propagated by vibrations in a plane
at any other angle to the principal section is resolved into two
such component rays. But the velocities of transmission in the two
directions are unequal, that is, the refractive index of the spar for
the two rays is different. If the analyzing nicol be so adjusted as to
receive the emergent light from the polarizer when the corresponding
planes of the two prisms are coincident when extended, the emergent
extraordinary ray falling into a plane of the same resistance as
that it had just left is propagated through the second nicol with
the same velocity that it passed the first one. It is therefore
similarly refracted. If, however, the two prisms be so arranged that
corresponding planes cross then the extraordinary ray falls into a
plane which it traverses with greater velocity than it had before and
is accordingly refracted and takes the course which ends in total
reflection at the film of balsam. No light therefore can pass through
the prism in that position. If any other substance, as for instance
a solution of sugar, capable of rotating a plane of polarized light,
be interposed between the two nicols the effect produced is the same
as if the analyzer had been turned to a corresponding degree. When
the analyzer is turned to that degree the corresponding planes again
coincide and the light passes. This is the principle on which the
construction of all polarizing instruments is based.[36]
=63. The Polariscope.=—A polariscope for the examination of solutions
of sugar consists essentially of a prism for polarizing the light,
called a nicol, a tube of definite length for holding the sugar
solution, a second nicol made movable on its axis for adjustment to
the degree of rotation and a graduated arc for measuring it. Instead
of having the second nicol movable, many instruments have an adjusting
wedge of quartz of opposite polarizing power to the sugar, by means of
which the displacement produced on the polarized plane is corrected.
A graduated scale and vernier serve to measure the movement of the
wedges and give in certain conditions the desired reading of the
percentage of sugar present. Among the multitude of instruments which
have been devised for analytical purposes, only three will be found
in common use, and the scope of this volume will not allow space
for a description of a greater number. For a practical discussion
of the principles of polarization and their application to optical
saccharimetry, the reader may conveniently refer to the excellent
manuals of Sidersky, Tucker, Landolt, and Wiechmann.[37]
=64. Kinds of Polariscopes.=—The simplest form of a polarizing
apparatus consists of two nicol prisms, one of which, _viz._, the
analyzer, is capable of rotation about its long axis. The prolongation
of this axis is continuous with that of the other prism, _viz._, the
polarizer. The two prisms are sufficiently removed from each other to
allow of the interposition of the polarizing body whose rotatory power
is to be measured.
For purposes of description three kinds of polarimeters may be
mentioned.
1. _Instruments in which the deviation of the plane of polarization is
measured by turning the analyzer about its axis._
Instruments of this kind conform to the simple type first
mentioned, and are _coeteris paribus_ the best. The Laurent, Wild,
Landolt-Lippich, etc., belong to this class.
2. _Instruments in which both nicols are fixed and the direction of the
plane of polarized light corrected by the interposition of a wedge of a
solid polarizing body._
Belonging to this class are the apparatus of Soleil, Duboscq,
Scheibler, and the compensating apparatus of Schmidt and Haensch.
3. _Apparatus in which the analyzer is set at a constant angle with
the polarizer, and the compensation secured by varying the length or
concentration of the interposed polarizing liquid._
The apparatus of Trannin belongs to this class.
=65. Appearance of Field of Vision.=—Polarimeters are also classified
in respect of the appearance of the field of vision.
1. _Tint Instruments._—The field of vision in these instruments in
every position of the nicols, except that on which the plane of
vibration of the polarized light is coincident with the three principal
sections, is composed of two semi-disks of different colors.
2. _Shadow Instruments._—The field of vision in this class of
polarimeters in all except neutral positions, is composed of two
semi-disks, one dark and one yellow. As the neutral position is
approximated the two disks gradually assume a light yellow color, and
when neutrality is reached they appear to be equally colored.
The Laurent, Schmidt and Haensch shadow and Landolt-Lippich
instruments, are of this class.
3. _Striated Instruments._—In this class the field of vision is
striated. The lines may be tinted as in Wild’s polaristrobometer or
black, as in the Duboscq and Trannin instruments. The neutral position
is indicated either by the disappearance of the striae (Wild) or by the
phenomenon of their becoming continuous. (Duboscq, Trannin.)
=66. Character of Light Used.=—Polariscopes may be further divided into
two classes, based on the kind of light employed.
1. _Instruments which Use Ordinary White Light._—(Oil lamp, etc.)
Scheibler, Schmidt and Haensch.
2. _Instruments Employing Monochromatic Light._—(Sodium flame, etc.)
Laurent, Landolt-Lippich, etc.
=67. Interchangeable Instruments.=—Some of the instruments in common
use are arranged to be used either with ordinary lamp or gas light, or
with a monochromatic flame. Laurent’s polarimeter is one of this kind.
The compensating instruments also may have the field of vision arranged
for tints or shadows. Theoretically the best instrument would be one in
which the light is purely monochromatic, the field of vision a shadow,
and the compensation secured by the rotation of the second nicol.
The accuracy of an instrument depends, however, on the skill and care
with which it is constructed and used. With quartz wedges properly
ground and mounted, and with ordinary white light, polariscopes may be
obtained which give readings as accurate as can be desired.
Since many persons are more or less affected with color-blindness, the
shadow are to be preferred to the tint fields of vision.
For practical use in sugar analysis the white light is much more
convenient than the monochromatic light.
For purposes of general investigation the polarimeters built on
the model of the laurent are to be preferred to all others. Such
instruments are not only provided with a scale which shows the
percentage of sucrose in a solution, but also with a scale and vernier
by means of which the angular rotation which the plane of vibration has
suffered, can be accurately measured in more than one-quarter of the
circle.