PARTIAL POLARIZATION.

361

the light be of sufficient intensity to penetrate such a mass of glass.

528. If the reflecting plate P (523) were placed at any other angle except that for complete polarization, still a certain portion of the reflected light will be polarized. Very different opinions have been hazarded on the nature of this partially polarized light; it has been, by several very illustrious philosophers, considered as made up of common light (518), mixed with a small quantity of completely polarized light. Sir David Brewster, to whom science is so largely indebted for his investigations on this subject, however, considers that partially polarized, or, as he proposes to call it, apparently polarized light, is light whose planes of polarization are inclined at angles of less than 90°; and he bases this opinion on the fact that light thus partially polarized may, by a sufficient number of reflections, have its planes of polarization turned round so as to coincide, and constitute perfectly polarized light. The following table, given by Sir David,* shows the number of reflections required to completely polarize light at any angle:

Number of reflections Angles at which the light is

required.

reflected.

529. Sir David Brewster illustrates his position by assuming a beam of common light to be constituted as NS, CD, (fig. 1, 517). Let such a beam be incident on a reflecting surface, so that the plane of reflection exactly bisects the

Optics, p. 173, and Phil. Trans., 1829.

angle which the two planes of polarization form with each other, as the dotted line AB besects the angles NTC and DTS (fig. 1). By reflection from a glass-plate, whose index of refraction is 1.525, the inclination Ns to AB will

1

be 33° 13'; so that DC will describe with NS angles of 66·26, as in fig. 2. At an incidence of 65, the inclination of Ns to CD will be 25° 36′; and at the polarizing angle of 56.45, the angle of inclination of ns, CD, will vanish, as the two beams are made to coincide as in fig. 3. Thus, at an incidence on glass at any angle differing from the polarizing angle of 56·45, the planes of light, NS, CD, become inclined more and more to each other, in proportion as the incident angle approaches 56-45, at which angle the two planes become so turned round as to coincide completely, and produce a single beam of polarized light.

530. In the preceding observations, light is supposed to be polarized by reflection from glass alone; the same physical characters may, however, be communicated to it by reflection from the surfaces of any non-metallic substance; as that reflected from metallic surfaces (553) differs in its properties from the polarized light under consideration. All bodies have their peculiar polarizing angle in the same manner as they have their index of refraction; thus, the angle for glass is 56° 45', and for water 52° 45'. The effects of the different polarizing angles of two transparent substances upon polarized light, may be shown by an experiment described by Sir D. Brewster. Having fixed the plates PR (524, fig. 2) at the angles of 56. 45', and with the planes of reflection and polarization perpendicular to each other, the image of the candle will be invisible in R (524). Breathe upon the latter, so as to cover it with a film of water, and immediately the candle will become visible, from a portion of the polarized beam undergoing reflection from R.

531. The angle of complete polarization for any substance, may be readily determined by the fact, discovered by Sir

POLARIZATION OF HOMOGENEOUS LIGHT.

363

D. Brewster, that:-The index of refraction is the tangent of the angle of polarization. Thus, if the polarizing angle of water, whose index of refraction is 1.336, be required, all that we have to do, is to look for that number in a table of natural tangents, or for its logarithm in a table of logarithmic tangents, and the corresponding angle of 53° 11' will be found opposite to either. The polarizing angle of crown-glass is 56° 45'; fcr, as its index of refraction is 1·525, the logarithm of that number is 18327, which in the table of logarithmic tangents, corresponds very nearly to the angle mentioned.

532. Light may be polarized by reflection from the second surface of bodies, or internal reflection (448); and the angle for complete polarization has its cotangent equal to the index of refraction of the substance, and may be found by looking for the latter number in a table of cotangents. This, in the case of water, will be 36° 49′, and of crown-glass 33° 15′; so that the polarizing angle at the second surface, is equal to the complement of that for the first surface of a medium.

533. If, instead of using white light, any one of the coloured beams of the spectrum (467) be incident on a reflecting medium, it will undergo polarization in the same manner as common light, but at a different angle for each ray. The value of the polarizing angle for each, may be found from its index of refraction (445), by means of the law of tangents (531). Thus, the polarizing angle, when water is used, is 53.4 for the red, and 53·19 for the violet beams; and when plate-glass is employed, 56·34 for the red, and 56.55 for the violet.

From the data contained in Fraunhofer's table (481), the polarizing angle for each of his seven rays may be readily computed.

534. As a considerable portion of light passes through a single glass-plate and is lost (524); when the reflecting surface is composed of but one plate, too small a quantity of polarized light for many purposes is procured. The frame CD (523)

should, therefore, contain about a dozen plates of thin glass, instead of only one, and then a very powerful beam of polarized light is obtained; and whenever the Polariscope is referred to in the following pages, it is always supposed to contain these number of glass-plates in the lower frame. If light be incident obliquely on the first plate of such a series, as at an angle of 74°, the refracted light will be almost entirely polarized, and in a plane at right angles to that of the reflected beam (527). A bundle of plates of mica, or talc, may be advantageously substituted for those of glass, as they are very light, occupy but little space, and polarize light very effectually (546).

535. When the sky is tolerably free from clouds, a certain portion of the light becomes more or less polarized in its passage to the earth. The maximum of polarization takes place about 90° from the sun. According to Arago, the rays reflected from the moon contain a considerable portion of polarized light.

in a circle placed

CHAPTER XXIV.

POLARIZED LIGHT.

Interference of Waves of Polarized Light, 536-Colours produced by, 537-varied by revolving the Crystal, 538-by revolving the Analyzing Plate, 539. Complementary Rings in Crystals with one Axis, 541. Negative and Positive Systems, 542. Rings in Crystals with two Axes, 543. Complementary Tints in unannealed Glass, 544-5. Analyzis of Refracted Rays, by Plates of Agate, Tourmaline, Mica, or Glass, 546. System of Rings in Compressed Jelly, 547—in Crystalline Lenses, 548. Circular Polarization, 549. Circular Polarization in Organic Fluids, 550. Formula for Molecular Force of Rotation, 551. Conversion of Rectilinear into Circular Polarized Light, 552. Elliptic Polarization, 553. Dichroism exhibited by Polarized Light, 554.

536. HAVING described some of the most important properties of white rectilinearly polarized light, we have next to investigate some of the phenomena of colour produced by interference. To appreciate these, the following laws, discovered by M M. Arago and Fresnel, must be previously well understood.

(A.) Two beams of light polarized in the same plane, are capable of interfering with each other like common light (486), and they produce in consequence fringes of the same character.

All the experiments on diffraction (489), if repeated with polarized light, will produce the same phenomena as if common light were used.

(B.) Two beams, polarized in planes at right angles to each other, will not by their interference produce colours. When polarized at angles intermediate, between 0° and 90°,