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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.
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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
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" 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
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⁄ ⁄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
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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