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Fig. 32-3. lllustration of the origin of the polarization of radiation |
scattered at right angles to the incident beam. |
There is a substance called polaroid which has the property that when light |
goes throuph it, only the piece of the electric fñeld which is along one particular |
axis can get throupgh. We can use this to test for polarization, and indeed we fnd |
the light scattered by the hypo solution to be strongly polarized. |
--- Trang 569 --- |
MPolqrr=crfiort |
33-1 The electric vector of light |
In this chapter we shall consider those phenomena which depend on the fact |
that the electric fñeld that describes the light is a vector. In previous chapters |
we have not been concerned with the direction of oscillation of the electric field, |
except to note that the electric vector lies in a plane perpendicular to the direction |
of propagation. The particular direction in this plane has not concerned us. We |
now consider those phenomena whose central feature is the particular direction |
of oscillation of the electric field. |
In ideally monochromatic light, the electric ñeld must oscillate at a defnite |
frequency, but since the z-component and the -component can oscillate indepen- |
dently at a defnite frequency, we must first consider the resultant efect produced |
by superposing two independent oscillations at right angles to each other. What |
kind of electric field is made up of an zø-component and a -component which |
oscillate at the same frequency? If one adds to an z-vibration a certain amount of |
u-vibration at the same phase, the result is a vibration in a new direction in the |
-plane. Figure 33-1 ïllustrates the superposition of diferent amplitudes for the |
z-vibration and the g-vibration. But the resultants shown in Fig. 33-l are not |
the only possibilities; in all of these cases we have assumed that the z-vibration |
and the -vibration are ?w phøse, but it does not have to be that way. It could |
be that the z-vibration and the z-vibration are out of phase. |
'When the z-vibration and the z-vibration are not in phase, the electric field |
vector moves around in an ellipse, and we can illustrate this in a familiar way. lÝ |
we hang a ball from a support by a long string, so that it can swing freely in a |
horizontal plane, it will execute sinusoidal oscillations. If we imagine horizontal |
z- and -coordinates with their origin at the rest position of the ball, the ball |
can swing in either the zø- or -direction with the same pendulum frequency. |
By selecting the proper initial displacement and initial velocity, we can set the |
--- Trang 570 --- |
" x / x ⁄ x |
Ey„ =1 Ey =1 Ey =1 |
E,=0 E,=Ÿ E,=1 |
Ey„ =0 E„= 1 Ey„ =—1 |
E,=1 E,=—1 E,= 1 |
Fig. 33-1. Superposition of x-vibrations and y-vibrations in phase. |
ball mm oscillation along either the z-axis or the -axis, or along any straight |
line in the zz-plane. 'Phese motions of the ball are analogous to the oscillations |
of the electric field vector illustrated in Fig. 33-1. In each instance, since the |
z-vibrations and the -vibrations reach their maxima and minima at the same |
time, the z- and -oscillations are in phase. But we know that the most general |
motion of the ball is motion in an ellipse, which corresponds to oscillations In |
which the zø- and ¿-directions are øøf in the same phase. “The superposition of #- |
and ø-vibrations which are not in phase is illustrated in Fig. 33-2 for a variety |
of angles bebween the phase of the z-vibration and that of the g-vibration. he |
general result is that the electric vector moves around an ellipse. The motion in |
a straight line is a particular case corresponding to a phase difference of zero (or |
an integral multiple of z); motion in a circle corresponds to equal amplitudes |
with a phase diference of 90° (or any odd integral multiple of z/2). |
In Eig. 33-2 we have labeled the electric field vectors in the ø- and z-directions |
with complex numbers, which are a convenient representation in which to express |
the phase diference. Do not confuse the real and imaginary components of the |
complex electric vector in this notation with the z- and +-coordinates of the fñeld. |
The z- and -coordinates plotted in Fig. 33-1 and Fig. 33-2 are actual electric |
felds that we can measure. The real and imaginary components of a complex |
--- Trang 571 --- |
⁄ ⁄2 G3 |
Ey = cosuf; 1 COS0f; 1 COS0f; 1 |
Ey = cosuf; 1 cos (0£ + T); eix/4 —sinwt; ï |
SN NY SN |
Exy = COSUf; 1 COSUf, 1 COS UŸf; 1 |
Ey = cos († + ei3x/4 — Cosưf; —1 — CoS (U£ + T); —e!⁄4 |
E,—=cosuf; 1 COS f; 1 cos(uf; 1 |
Ey„ =sinuwf; —i — Cos (f + Š*); —el3”/4 cosœf; 1 |
Fig. 33-2. Superposition of x-vibrations and y-vibrations with equal |
amplitudes but various relative phases. The components Ex and Ey are |
expressed In both real and complex notations. |
electric ñeld vector are only a mathematical convenience and have no physical |
significance. |
NÑow for some terminology. Light is ¿mearlJ polarized (sometimes called |
plane polarized) when the electric feld oscillates on a straight line; Eig. 33-1 |
iHustrates linear polarization. When the end of the electric field vector travels In |
an ellipse, the light is ellticall polarizcd. When the end of the electric feld |
vector travels around a cirele, we have c¿rcular polar?zation. TỶ the end of the |
electric vector, when we look at it as the light comes straight toward us, goes |
around in a counterelockwise direction, we call it right-hand cireular polarization. |
Figure 33-2(ø) illustrates right-hand circular polarization, and Fig. 33-2(c) shows |
--- Trang 572 --- |
left-hand circular polarization. In both cases the light is coming out of the paper. |
Our convention for labeling left-hand and right-hand circular polarization is |
consistent with that which is used today for all the other particles in physics |
which exhibit polarization (e.g., electrons). However, in some books on optics |
the opposite conventions are used, so one must be careful. |
W©e have considered linearly, cireularly, and elliptically polarized light, which |
covers everything except for the case of wnpolarizcd light. NÑow how can the light |
be unpolarized when we know that it must vibrate in one or another of these |
ellipses? If the light is not absolutely monochromatie, or if the z- and -phases |
are not kept perfectly together, so that the electric vector first vibrates in one |
direction, then in another, the polarization is constantly changing. Remember |
that one atom emits during 10~Ẻ sec, and if one atom emits a certain polarization, |
and then another atom emits light with a diferent polarization, the polarizations |
will change every 10” sec. TỶ the polarization changes more rapidly than we |
can detect i%, then we call the light unpolarized, because all the efects of the |
polarization average out. None of the interference effects of polarization would |
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