Page images
PDF
EPUB

LONDON, EDINBURGH, AND DUBLIN

PHILOSOPHICAL MAGAZINE

AND

JOURNAL OF SCIENCE.

[FOURTH SERIES.]

MAY 1874.

XXXIX. On the Determination of the prime Angle of Incidence and prime Azimuth for the different Fraunhofer's Lines. By G. QUINCKE*.

IF

F under the prime angle of incidence H linearly polarized light be reflected from a plane surface, the plane of polarization making the angle a with the plane of reflection, the two components polarized perpendicular and parallel to the plane of incidence will have a difference of phase of a quarter wave-length, and the ratio of their amplitudes is determined by the tangent of the prime azimuth B, by the equation

[blocks in formation]

The reflection is named positive when the component polarized parallel to the reflection-plane is accelerated relatively to that polarized perpendicular to that plane, negative when it is retarded. The former case is the more frequent. With metals, positive reflection only has yet been observed.

If the prime angle of incidence and prime azimuth are known, then from these the difference of phase and the ratio of the amplitudes, or the intensity of the components of the reflected light, for any angle of incidence can be calculated by means of formulæ which, although of quite a different form and found in a very different way, represent the phenomena equally well, within the possible errors of observation. (Conf. Pogg. Ann. vol. cxxviii. pp. 387-399, 541-564. 1866; vol. cxxxvi. p. 585. 1869.)

* Translated from a separate impression, communicated by the Author. Phil. Mag. S. 4. Vol. 47. No. 313. May 1874. Y

The prime angle of incidence and azimuth are thus determined :-The difference of phase of the two components polarized parallel and perpendicular to the plane of incidence are, in any way, made equal to a high multiple of ± The two then give

λ

2

linearly polarized light, which being extinguished by an analyzing Nicol prism, its plane of polarization can thus be determined.

The light originally polarized linearly, and after reflection elliptically polarized, can be converted into linearly polarized (1) by being again reflected once or more times under the same conditions, (2) by annihilating the difference of phase by a plate of crystal of variable thickness (a plate of cale spar cut perpendicular to the optic axis, a Babinet's compensator) whose principal section coincides with the plane of reflection, (3) by turning the principal section of a crystal plate of invariable thickness (a plate of mica of toward the reflection-plane.

The first method has been used by Brewster* and Jamin†; the second by Brewster*, Jamin ‡, Van der Willigen §, Haughton ||, and me; the third by De Sénarmont**, Kirchhoff, and Eilhard Wiedemann ++.

upon

The most perfect process is that adopted by Jamin, who threw a pure (objective) spectrum with Fraunhofer's lines a polarizing Nicol in azimuth 45°, and with the analyzing Nicol in azimuth 8 extinguished the rays twice reflected under the prime angle of incidence H by parallel mirrors. The angle of incidence and azimuth ẞ were altered until the field appeared as dark as possible.

Azimuth B is then given by the equation

B= = arc (tan =√tan ß).

[ocr errors]

(2)

Jamin determined in this way the optical constants of several metals for different Fraunhofer lines, and thence deduced the various colours of the metals.

This procedure has many inconveniences, especially this, that the angle of incidence cannot be determined with sufficient accuracy. A slight modification of it, which I have employed for more than ten years, consists essentially in observing the spec

* Phil. Trans. 1830, pp. 294 & 312.

† Ann. de Chim. (3) vol. xxii. p. 311 (1848). Ibid. vol. xxix. p. 281 (1850).

Pogg. Ann. vol. cxvii. p. 464 (1862).

Phil. Trans. 1863, p. 122.

Pogg. Ann. vol. cxxviii. pp. 355 & 541 (1866).

** Ann. de Chim. (2) vol. lxxiii. p. 337 (1840).

†† E. Wiedemann, Elliptische Polarization des Lichtes. Leipzig: 1872.

trum with Fraunhofer's lines not objectively, but subjectively, and permits the prime angle of incidence and prime azimuth to be determined with any accuracy desired, as soon as reflecting surfaces generally can be produced of homogeneous quality.

Through a collimator with a vertical slit and an achromatic lens, a pencil of parallel rays falls upon a polarizing prism standing in the azimuth 45°, and then upon a horizontal astronomical auxiliary telescope, the cross-threads of which can be illuminated by a plane glass (between the eyepiece and the crossthreads) inclined 45° to the axis of the telescope.

Across the slit of the collimator runs a thin wire, to which the cross-thread of the telescope is adjusted. It lies on the axis of the collimator when its position is unaltered on turning the latter 180°.

Between the collimator and the telescope is a large smoothed cast-iron frame, on which an iron sledge with a horizontal circle can be moved parallel to itself. A little table in the centre of the circle, and the circle itself, are to be moved each by three adjusting-screws, and the rotation of the table to be measured by two diametral verniers. On the table a plane-parallel glass is fixed, so that the image of the cross-threads of the telescope is reflected towards the latter. When the plane glass is rotated 180° the cross-threads and their image again coincide, if the axis of rotation of the circle is normal to that of the collimator. The normal of the plane glass and the axis of the collimator then coincide; the angle of incidence is 0°.

The azimuth 90° of the polarizing Nicol is determined thus :— The slit of the collimator is illuminated with daylight or with a sodium-flame, the angle of incidence made nearly equal to the angle of polarization, and the glass plate and the polarizing Nicol rotated until the image of the slit, observed with the naked eye or a telescope, shows a minimum intensity of light (0).

The analyzing Nicol, fixed on a vertical circle, stood at 0° when, after the removal of the plane glass, the light issuing from the strongly illuminated slit, and polarized by the Nicol in the azimuth 0°, was completely extinguished.

The vertical circle with the analyzing Nicol could either be moved parallel to itself on a horizontal plane table-plate, or it was fastened in front of the objective of a telescope which was directed to the slit of the collimator and could be moved parallel to itself on a cast-iron sledge with a frame, like the horizontal circle.

Between the eye and the analyzer I brought a flint-glass prism of from 30° to 60° refracting angle with a vertical edge, or a system of prisms for direct vision. The light from the slit of

the collimator gives then a horizontal spectrum with Fraunhofer's lines of from 1° to 3° breadth.

On the table of the horizontal circle, instead of the plane glass, two parallel plane mirrors of the substance to be examined are fastened with their ends overlapping, so that one of them by reflection of the cross-threads can be placed perpendicular to the axis of the auxiliary telescope or the collimator, and its parallelism be tested by turning it through 180°. The mirrors were, by means of the arrangement described in Pogg. Ann. vol. cxlii. p. 198, pl. 5. fig. 3, placed parallel, being fastened with wax on the two sledges, the faces pressed against each other, and the sledges drawn asunder.

Frequently they were only fastened with wax upon a horizontal glass plate, and one of the mirrors rotated until the twice reflected image of a distant object (a tree on the horizon) was coincident with the object itself.

If from a heliostat sunlight be let through the slit of the collimator, and polarized in the azimuth ±45°, to the parallel mirrors, and the light reflected under the prime angle of incidence be taken up by the analyzing Nicol in the azimuth ß, a dark streak appears in the spectrum, which can be made to fall on a determined Fraunhofer line by changing the angle of incidence H and the azimuth B. The reading of the incidence-angle gives directly the prime angle of incidence H for the Fraunhofer line in question, and equation (2) the corresponding prime azimuth.

From the determinations with positive and negative angles of incidence and positive and negative azimuths the mean was taken.

The defects of the method consist in the difficulty of obtaining Nicol prisms with even surfaces, which, brought in front of the objective of the collimator and the telescope, would give distinct images of the slit, and, further, that the incident and the issuing ray make with each other an angle which may amount to as much as 1o. For this reason I have mostly omitted the observing telescope between the eye and the analyzer.

On turning the polarizing Nicol from the azimuth +45° to -45° the image of the collimator-slit was displaced towards the cross-thread of the auxiliary telescope -8', as shown by the image of the thread reflected by the plane glass. This alteration of the angle of incidence 8' had to be taken into account in

the determination of H.

The divisions of the circle were read with verniers accurately to l'. The error of a single determination of H or ẞ scarcely amounts to 1', if the reflecting surface is even and homogeneous and has at all parts the same optical constants H and B.

Variations of temperature, however, and pressure in polishing

frequently alter the optical qualities of a mirror very considerably; and it is probably much more difficult to obtain faultless reflecting surfaces than transparent substances free from veins. Besides these irregularities, disturbance is occasioned by unavoidable scratches and roughnesses of the surface, which act like a diffraction-grating. As in the case of coefficients of elasticity or electric conducting-power, properly the value of H and B must be determined for each definite portion.

The following Table (p.326) contains a series of determinations of the prime angle of incidence and prime azimuth for Fraunhofer's lines C, D, E, F, and G, executed by the method of parallel mirrors; and the numbers in general, so far as they relate to substances previously investigated, agree with the above-mentioned measurements by Jamin and Haughton.

The gold was burned in upon plate glass by heating a solution with essential oil; copper and nickel were electro-deposited; the cobalt consisted of polished pieces such as occur in commerce. Antimony, bismuth, zinc, and tin were cast and polished plates; aluminium, brass, and platinum were rolled; the silver was obtained by Martin's process (Pogg. Ann. vol. exxix. 1866, p. 55) from a solution several months old.

For reflection in glass, the silver was fixed on the long, parallel sides of two Fresnel parallelepipeds, which had an acute angle of 56° 52' and the exponents of refraction

[blocks in formation]

1.5220 1.5246 1.5279 1.5308 1.5362

In the calculation of the prime azimuths, account is taken of the rotation of the plane of polarization on the entrance into and the issue from the glass. To the selenium a reflecting surface had been imparted by pressing cold plates of glass on the melted substance.

The most perfect surfaces were possessed by nickel, silver, gold, and selenium.

Where not stated otherwise, the reflection took place in air; and shortly before the observation the metals had been polished with clear buckskin and a trace of jeweller's rouge.

With the exception of gold, in the case of all the metals here mentioned the prime angle of incidence (polarization-angle) diminishes with the diminution of the wave-length-the reverse of what takes place with transparent bodies. The diminution, however, is very different with the different metals.

The prime azimuths partly increase, and partly diminish as the wave-lengths become less. Platinum shows a maximum value for the line D, cobalt and bismuth for the line E, and tin for the line F.

« PreviousContinue »