234

POLARIZATION BY REFLECTION.

[119.

plate is made to describe a quarter of a rotation in its own plane, 2; the axes of the two plates are then at right angles to each other in all intermediate positions, light will be transmitted with greater or with less intensity, according as the axes are more nearly parallel, or perpendicular to each other.*

If the two beams emerging from a rhombohedron of Iceland spar be examined by means of a plate of tourmaline, it will be found that the ordinary image is most intense when the axis of the tourmaline is at right angles to the principal section of the rhombohedron, and that it is extinguished when the axis of the tourmaline is parallel to the principal section, whilst the opposite results occur with the extraordinary ray. Both rays are therefore polarized, but under different circumstances.

(120) Polarization by Reflection.-Polarization may also be effected by means of reflection. Whenever light is reflected from the surface of a transparent medium, a certain portion of such light undergoes this remarkable change; and at a particular angle, varying with each medium according to its refractive index, the whole of the incident light that is reflected is polarized. This effect takes place when the reflected and the refracted ray are at right angles to each other: consequently the greater the refractive index the greater is the polarizing angle: with crown glass this angle is 56° 45', with water 53° 11', and with Iceland spar 58° 51'.

When light which has been polarized by any of these means is examined by a reflecting plate, inclined to the ray at the polarizing angle, other remarkable properties are observed. Common light will be reflected indifferently, whether the reflecting plate be placed above or below the ray, to the right or to the left of it, though the inclination of the plate to the ray continue to be the same. It is not so with polarized light; suppose a beam thus affected to fall upon any transparent reflector inclined to the ray at the polarizing angle; if the light be completely reflected when the mirror is placed below the ray, it will not be reflected at all, but be wholly transmitted when the plate is placed on either side, and when placed above, it will again be wholly reflected; at intermediate points part will be reflected and the remainder transmitted; the portion which is reflected is greater the more nearly the plane of the second reflection coincides with that of the first,

* When such a plate of tourmaline is rendered incandescent, the light which it emits is partially polarized, but it is polarized in a plane at right angles to that of the polarized beam which it transmits.

120.]

POLARIZATION BY REFLECTION.

235

the light being wholly transmitted when the two are at right

angles to each other.

These facts admit of easy experimental proof. Provide two tubes, B, C (fig. 101), which are fitted so as to allow of their being turned round one within the other. Fasten obliquely to the end of each tube a flat transparent plate of glass, P, A, so as to form an

B

FIG. IOI.

FIG. 102.

angle of 56° 45′ between the line p a, and a perpendicular to the point at which pa falls upon the surface of each plate. The tube B, with its attached plate ▲, can now be turned round on the tube c, without altering the inclination of the plate to a ray passing along the axis of the two tubes; but the plate A, according to its position, will reflect the ray upwards or downwards, to the right or to the left. We can, therefore, alter the plane in which the reflection is produced, without altering the angle of the reflector to the ray. If the light be common light, such as that from a candle placed as at J, no matter whether the plate A be placed below the ray as in fig. 101, or above it as in fig. 102, or to the right or to the left, an observer placed in the direction which the reflected ray, 0, would follow, would see the candle distinctly: but the case would be different if the candle were placed as at 1, where the light would be reflected from the plate P, along the axis of the tubes; by reflection at this particular angle it would be in great measure polarized. So long as the plate A

B

C

retains the position represented in fig. 101, the reflected ray would fall in the same plane as that in which polarization took place, and the candle would be But supseen by an observer stationed in the direction of the reflected ray.

pose the tube B to be turned slowly round the ray; by following the image as the tube is turned, the light of the candle will be seen to become gradually fainter and fainter, until, when the tube has been turned a quarter of the way round, it will be almost invisible; the plane of reflection is now at right angles to that of polarization, and the light which falls upon ▲ is almost wholly transmitted on turning it further, the light becomes more and more distinct, till, when the tube has been turned half round, the candle is seen as brightly as at first; the plane of reflection again coincides with that of polarization; if it be turned still further, at the third quadrant the light again disappears, until, on completing the revolution, it is as distinctly visible as at first.

The plane of incidence, or the plane of reflection in which the polarization was produced, is called the plane of polarization. The original plane of polarization may be easily ascertained in any ray, by whatever means it may have been polarized, because it is always at right angles to the plane in which extinction occurs when the ray is examined by a reflecting glass mirror, inclined to the ray

236

POLARIZATION OF LIGHT.

[120. at the polarizing angle. In this manner it is proved not only that the doubly refracted rays transmitted by Iceland spar are each polarized, but that they are polarized in planes at right angles to each other, the ordinary ray being polarized in the plane of the principal section: in the case of tourmaline, it is found that the emergent ray is polarized in a plane perpendicular to the axis of the crystal.

When the condition of polarization has once been impressed upon a beam of light, it continues to be permanent, whether the subsequent course of the ray be long or short, provided it continue in a homogeneous medium.

(121) Distinction between Common and Polarized Light.Every beam of common light appears to consist of a rapid succession of systems of waves, each system undulating in a determinate plane, always at right angles to the direction pursued by the ray; but the inclination of this plane in one system varies at all possible angles with the plane of vibration in the preceding and succeeding systems. As a resultant of these various motions, common light may be regarded as composed of two beams of light which are vibrating in planes at right angles to each other. Polarized light differs from ordinary light in being produced by vibrations in a single plane only, that plane being perpendicular to the plane of polarization; and the phenomenon of polarization consists simply of the resolution of the vibrations of common light into two sets, in two rectangular directions, and the subsequent separation of the two systems of waves thus produced' (Lloyd, Wave Theory of Light, 3rd Edit. 1873, 169). The effect of a crystal of Iceland spar upon common light will be best understood by considering its action upon a beam which has been already polarized. When a beam of light polarized in any given plane falls upon a crystal of Iceland spar, it is split into two portions, the relative intensity of which varies with the inclination of the plane of polarization to the principal section of the crystal, one beam vanishing altogether when the other is at a maximum. Now common light consists of successive systems of waves, each system being in the condition of a polarized beam; for its vibrations occur in one definite plane. When the undulations belonging to one of these systems fall upon the spar, they are divided into two beams of unequal intensity, but owing to the extremely brief duration of each system, the beams produced by several hundred of these systems in succession are simultaneously (so far as the eye can perceive) thrown upon the same spot; the greater intensity of the light produced by some of these systems compensates for

124.]

VARIOUS PHENOMENA OF POLARIZED LIGHT.

237

the feebler intensity of others, and the resultant effect is the production of two beams which are of equal intensity whatever be the position of the spar. The result of the analysis is the same as that which would have been yielded by a compound ray, consisting of two other rays polarized in planes at right angles to each other, one plane coinciding with the principal section of the crystal, and the other being at right angles to it.

Since the vibrations of a polarized ray always occur in the same plane, we may, with the assistance of a rude illustration, form some idea of the reason why it appears to be possessed of sides. If we imagine the reflecting surface to be made up of a series of parallel fibres lying only in one direction, these fibres would allow the passage of all the rays in common light which undulate in a plane parallel to their direction, and would reflect the rest whilst polarized light, if undulating in a plane parallel to the fibres, would be wholly transmitted; but if its undulations were in a plane at right angles to the fibres it would be wholly reflected.

FIG. 103.

(122) Polarization by Bundles of Plates.-Light may also be polarized at other angles by a series of successive reflections from several transparent plates: a pile of glass plates, as shown at fig. 103, is often made use of for this purpose; part of the light is transmitted whatever may be the angle of incidence: but the light polarized by reflection is always equal in quantity to that which is polarized by transmission, and it is polarized in a plane at right angles to it.

(123) Rotation of Plane of Polarization by Analyser.-In all cases where a polarized beam is received on a reflecting or analysing surface, the plane of reflection of which does not coincide with the plane of polarization, the plane of polarization becomes changed. The rotation of the plane of polarization is always towards that of reflection, and the amount of this rotation depends upon the angle of incidence which the ray forms with the analysing plate. If the light be incident upon the analysing plate at the polarizing angle, the plane of polarization is brought to coincide with that of reflection; but the rotation of the plane of polarization is less in proportion as the angle of incidence differs more from the polarizing angle. A corresponding alteration in the plane of polarization is effected by refraction upon the transmitted beam, but it is in an opposite direction.

(124) Colours of Polarized Light.-When a beam of polarized light is transmitted in particular directions through plates of doubly refracting bodies, and the light examined by an analyser, a series of splendid phenomena are observed, dependent upon the production of colours, which vary with the circumstances of the

238

:

COLOURS OF POLARIZED LIGHT.

[124.

experiment. The simplest method of rendering these colours visible consists in adjusting two reflectors, so that the image polarized by reflection from the first may be extinguished in the second. The first is called the polarizing, the second the analysing plate in the above mentioned position the polarizer and analyser are said to be crossed. By introducing a thin plate of any doubly refracting substance, such as mica, quartz, or selenite, cut in a direction parallel to that of the optic axis, the image suddenly reappears in the analysing plate, but it is tinged of a particular colour. If while the ray falls perpendicularly on the interposed plate, the plate be turned round in its own plane, two positions will occur in which the image completely disappears; these positions are at right angles to each other. In one, the principal section of the plate coincides with the plane of polarization, and in the other it is perpendicular to it. The colour does not change during this rotation, but only varies in intensity. When ordinary unpolarized light traverses such a doubly refracting film, the ray is split into two, the vibrations of which are at right angles to one another; but when polarized light meets with a doubly refracting surface, in such a position that the plane of vibration of the polarized ray coincides with one of the planes of vibration of the crystal, the light is transmitted without change, but the light so transmitted is stopped by the analyser. When the crystal is rotated through 90°, the plane of the polarized ray coincides with the other plane of vibration of the crystal, and the light is stopped by the analyser as before. But if the crystal remain fixed, and the analysing plate be made to rotate, the colour will pass through every grade of the same tint, into the complementary colour, and at each succeeding quadrant the hue is exactly complementary to that which was exhibited in the preceding one. When the polarizer and analyser are parallel, and the plane of vibration of the polarized beam coincides with one of the planes of vibration of the crystal, the light is transmitted without change, and consequently is not stopped by the analyser. The same result is observed when the crystal is rotated 90°: in both these positions the transmitted light is white. In intermediate positions of the crystal a different effect is produced; the polarized ray is then divided into two, vibrating in planes at right angles to one another, and one traversing the crystal at a lower velocity than the other. It will be the simplest to consider, in the first place, the result when the polarizer and analyser are crossed, and the crystal so placed that the planes of vibration of the two transmitted rays make angles of 45° with the plane of