Figs. 11 and 12 show the two prisms in their cases, the principal sections being indicated by b b m, b′ b' n, and the planes of polarization at right angles thereto, by a a m, a' a' n.

If we turn the analyzer A so that its plane of polarization aan is parallel with the plane of polarization a am of the polarizer P (Fig. 11), whereby, too, the principal sections bbm and b'b'n of the two prisms are brought into the same direction, the ray m, which enters P as ordinary light and emerges polarized at n, is not decomposed on passing through A. It is merely slightly refracted in

the direction of an extraordinary ray m p q (Fig. 10), and emerges so at the opposite end of the analyzer. The same happens if the latter be turned through an angle of 180°, so as to bring the planes again parallel. But, if the analyzer is adjusted so that its plane of polarization is at right angles to that of the polarizer-that is, when the prisms are arranged as in Fig. 12-then the ray entering A takes the direction of an ordinary ray, like mor (Fig. 10), and is eliminated by the film of balsam. No light leaves the analyzer, and, accordingly, the field of vision appears dark. The same thing happens at a distance of 180°.

In all cases where the planes of polarization (or the principal

sections) of the two Nicols are neither parallel nor at right angles to each other, the polarized light entering the analyzer is separated into an ordinary and an extraordinary ray, varying in intensity with the angle at which the planes of polarization of the two prisms are inclined to each other. Suppose them at first to be crossed, that is, set for darkness. Then, if we turn the analyzer through a small angle, the luminous intensity of the laterally-deflected ordinary ray will greatly exceed that of the transmitted extraordinary ray. Nevertheless, the latter suffices to slightly illuminate the field of vision. If the angle be increased to 45°, the ordinary and extraordinary rays will be of equal intensity, so that the light leaving the analyzer will have exactly half the luminous power of the total entering light. By increasing the angle further, the luminous power of the transmitted ray will gradually exceed that of the eliminated ray, until at an angle of 90° the latter ceases altogether to exist, and the field of vision exhibits the maximum of brightness. Continuing the rotation in the same direction, we find another minimum of light at 180°, and another maximum at 270°.

Fig. 13.

§ 5. To observe these phenomena, the instrument shown in Fig. 13 may be used. The horizontal bar d, secured on a stand, carries at one end the fixed polarizing Nicol a, and at the other the analyzing Nicol b, which, by means of the lever c, can be turned with its frame about its axis. In connection with the lever, a single or a double index moves round the divided disc, I which is fixed to the bar. Between the Nicols can be inserted the tube f, the ends of which can be closed with glass plates.

We first direct the polarizer a towards some luminous source, and the phenomena are simplified by using monochromatic light, i.e., a Bunsen flame playing on a

Now, if we look through the analyzing Nicol while revolving it, we shall be able readily to find a position in which the field of vision appears darkest. Suppose the index now to be at the zero-point on the disc. Then, as explained above, on continuing the rotation we shall find, in a complete revolution, another maximum of darkness at 180°, and the two maxima of light at 90° and 270° respectively. For purposes of scientific observation, the points of greatest darkness are to be preferred as marks of reference, since at these points the least movement of the Nicol produces a perceptible change in the appearance of the field of vision.

P

Fig. 14.

A

a

§ 6. Now, if the tube be filled with a solution of cane-sugar instead of water and put in its place, the analyzer having been previously set to darkness (0° or 180°), it will be found that the field of vision now appears bright, and to obtain the maximum of darkness we must turn the analyzer to the right through a certain angle. If the plane of polarization of the fixed polarizer of the instrument has the direction P P (Fig. 14), so p' long as the tube is empty the rays cannot pass through the analyzer, since its plane of polarization A A' is at right angles to PP'. But, if after the introduction of the sugar solution the field of vision exhibits the maximum of darkness when the plane of polarization of the analyzer is revolved into the position aa', we are bound to conclude that the rays originally vibrating in the plane P P', in their passage through the solution, have experienced a certain deflection of their plane of vibration, and that their vibrations are now perpendicular to a athat is, they take place in the plane p p'.

a

The angle a, through which the analyzer has to be turned to bring a recurrence of darkness in the field of vision, and which can be read off on the graduated rim of the disc, is called the angle of rotation, and is the measure of the deflection experienced by the plane of polarization.

A number of other substances behave in the same way as canesugar-that is to say, the analyzer requires to be turned to the right hand from zero to reach the point where the light vanishes. Again, if the tube be filled with nicotine or a solution of amygdalin, the phenomenon of reappearance of light occurs as before; but, in this

case, to set the instrument back to darkness the analyzer has to be turned to the left. These substances, therefore, cause a deflection of the plane of polarization to the left.

This rotation of the plane of vibration, or of polarization, is called circular polarization. Substances which exhibit this power are said to be circular-polarizing or optically active, and are distinguished as right-rotating (dextro-gyrate) or left-rotating (lavo-gyrate), whilst those substances which have not this power are said to be inactive.

Circular polarization was first noticed in 1811 by Arago, in rockcrystal. In 1815 Biot discovered the optical activity of organic bodies, and in a series of important investigations, extending over more than forty years, he deduced the laws and explained the nature of the phenomena. His observations form the basis of our present knowledge of the subject.'

1 Biot: Mém. de l'Acad. 2, 41; 3, 177; 13, 39; 15, 93; 16, 299. Ann. Chim. Phys. [2] 9, 372; 10, 63; 52, 58; 69, 22; 74, 401; [3] 10, 5, 175, 307, 385; 11, 82; 28, 215, 351; 29, 35, 341, 430; 36, 357, 405; 59, 206.

NOTE BY TRANSLATOR.

For the sake of some readers, it may be as well to add here a rather more explicit account of the action of a piece of apparatus so fundamental in polariscopic work as the Nicol prism. Taking Fig. 1û in the text, let us add to the author's construction by drawing through m a both-ways perpendicular (normal) to a b', as also through p and › similar normals to db'. Now, in their passage through the first half of the prism, the rays are both bent towards the normal m n'1, (i.e., outward from the balsam), to extents due to their different refractive indices, the ordinary ray mo (refr. ind. 1·66) more than the extraordinary ray mp (refr. ind. 1·52). The refractive index for Canada balsam for mean light being 1·54, the extraordinary ray on meeting the line b' d' (which, to represent a layer of sufficient thickness, must be broadened into a rhomboid) here encounters a medium of refractive power almost identical with that of the calc-spar which it left, so that this ray passes on with but a minute deviation inwards, due to the balsam being slightly more refractive than the spar for this ray. On the other hand, the balsam being very considerably less refractive than the calc-spar for the ordinary ray, causes that ray to diverge outwards from the normal, on's, and so much so, that it cannot hold a course through the balsam at all, but, inasmuch as the angle of incidence mong in the more refractive medium exceeds the so-called critical angle, the ray suffers total reflection from the surface, so that the angle rong equals angle mon3. The critical angle, or 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. Simple geometrical considerations show that if the angle to the normal in the more refractive medium has a sine whose value is greater than the ratio of the absolute indices, the ray cannot emerge into the less refractive medium. Now, in the case before us the ratio in question for balsam and spar is

1.54 1.66

= 0.928 sin 68°.

Hence the limiting value of mo ng, so that mo might just emerge in direction o d', is 68°. If now mo were parallel to a d', the angle mon, would be just 68°, being opposite to

b'a d', which has been ground down to 68°-the figure ma d'ng in that case forming a parallelogram. But in passing through the first half of the prism, the ray is refracted

a

FIG. 10A,

=

so that the angle mong is always greater than bad'. Thus we see that by grinding the endfaces of the prism so that b'a d' 68°, we secure that the angle mong shall always exceed the critical angle, and the importance of this procedure in the construction of the prism becomes apparent. As to what happens when a second Nicol is used to receive the extraordinary ray emerging from the first, the following considerations may perhaps be found useful:-In all uniaxial crystals there are two directions at right angles to each other, the one of greatest resistance to the propagation of luminous vibrations, the other of least resistance. These planes are in the direction of the principal axis (see Fig. 5) and at right angles thereto. Calc-spar transmits only such light, the vibrations of which take place in either of these two directions; 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, since amount of refraction depends on velocity of transmission, the refractive index of the spar is, as we have already said, different in the two directions. Now if the second Nicol be arranged behind the first, so that corresponding planes in the two prisms be coincident (as in Fig. 11), the extraordinary ray, coming into a plane of the same resistance as that which it left, is propagated with the same velocity as it had in the first prism, and is, therefore, similarly refracted, i.e., it takes a

course similar to Imp q (Fig. 10) in the first Nicol, emerging unaltered.

If, however, the second prism be arranged so that corresponding planes shall cross, then the extraordinary ray, coming into a new plane in which it travels with greater velocity than before, is refracted accordingly, taking a course similar to mor (Fig. 10) in the first Nicol, i.e., is totally reflected, so that no light emerges. Lastly, if the planes of the Nicols be crossed at any other angle, the light cannot pass in the plane it encounters in the second Nicol, but is resolved into two components in the two directions at right angles to each other, in which alone (as we have said) calc-spar transmits light-vibrations-that component which takes the course of the principal section being eliminated by the Canada balsam, whilst that which takes a course at right angles thereto alone emerges. Now that reduction of intensity in luminous power which may be effected on a polarized ray emerging from one Nicol by opposing to its course an impassable plane of a second Nicol, is also effected by opposing to its course a rotatory substance. The ray is made to vibrate in a different plane; in other words, the plane of polarization is rotated, and the resulting phenomenon is the same as if the first Nicol had been rotated to the same extent. The physical explanation of this rotatory power is discussed in succeeding chapters.-[D. C. R.]