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beam is polarized in the plane of ineidence, there will be no refected light.
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¡ -Q08 ⁄Z
I + #
Fig. 33-4. Reflection of linearly polarized light at Brewster's angle.
The polarization direction ¡s indicated by dashed arrows; round dots
Iindicate polarization normal to the paper.
This phenomenon 1s readily demonstrated by reflecting a linearly polarized
beam from a flat piece of glass. lf the glass is turned to present diferent angles
of incidenee to the polarized beam, sharp attenuation of the refected intensity
is observed when the angle of inecidence passes through Brewster s angle. This
attenuation is observed only if the plane of polarization lies in the plane of
Incidenee. Tf the plane of polarization is normal to the plane of incidence, the
usual refected intensity is observed at all angles.
33-5 Optical activity
Another most remarkable efect of polarization is observed in materials com-
posed of molecules which do not have refection symmetry: molecules shaped
something like a corkscrew, or like a gloved hand, or any shape which, if viewed
through a mirror, would be reversed in the same way that a left-hand glove
reflects as a right-hand glove. Suppose all of the molecules in the substance are
the same, I.e., none is a mirror image of any other. Such a substance may show
an interesting efect called optical activity, whereby as linearly polarized light
passes through the substance, the direction of polarization rotates about the
beam axis.
To understand the phenomenon of optical activity requires some calculation,
but we can see qualitatively how the efect might come about, without actually
carrying out the calculations. Consider an asymmetric molecule in the shape
of a spiral, as shown in Eig. 33-5. Molecules need not actually be shaped like a
corkscrew in order to exhibit optical activity, but this is a simple shape which
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ị Z2 ⁄ Ex
01 zZ ZI+A "
Fig. 33-5. A molecule with a shape that ¡is not symmetric when
reflected in a mirror. A beam of light, linearly polarized in the y-direction,
falls on the molecule.
we shall take as a typical example of those that do not have reflection symmetry.
'When a light beam linearly polarized along the z-direction falls on this molecule,
the electric field will drive charges up and down the helix, thereby generating
a current in the z-direction and radiating an electric field l„ polarized in the
u-direction. However, if the electrons are constrained to move along the spiral,
they must also move in the z-direction as they are driven up and down. When
a current is ñowing up the spiral, it is also Ñowing into the paper at z = z1
and out of the paper at z = z¡ + A, if A ¡is the diameter of our molecular spiral.
One might suppose that the current in the z-direction would produce no net
radiation, since the currents are in opposite directions on opposite sides of the
spiral. However, if we consider the zø-components of the electric field arriving
at z = zs, we see that the field radiated by the current at z = z¡ + A and the
fñeld radiated from z = z¡ arrive at z¿ separated in time by the amount A/c,
and thus separated in phase by + œ4/c. Since the phase difference is not
exactly r, the two fields do not cancel exactly, and we are left with a small
#-component in the electric fñeld generated by the motion of the electrons in the
molecule, whereas the driving electric fñeld had only a -component. This small
#-component, added to the large -component, produces a resultant field that is
tilted slightly with respect to the -axis, the original direction of polarization.
As the light moves through the material, the direction of polarization rotates
about the beam axis. By drawing a few examples and considering the currents
that will be set in motion by an incident electric fñield, one can convince himself
that the existence of optical activity and the sign of the rotation are independent
of the orientation of the molecules.
Corn syrup is a common substance which possesses optical activity. The
phenomenon is easily demonstrated with a polaroid sheet to produee a linearly
polarized beam, a transmission cell containing corn syrup, and a second polaroid
--- Trang 580 ---
sheet to detect the rotation of the direction of polarization as the light passes
through the corn syrup.
33-6 The intensity of reflected light
Let us now consider quantitatively the relection coeffcient as a function of
angle. Pigure 33-6(a) shows a beam of light striking a glass surface, where it
1s partly reflected and partly refracted into the glass. Let us suppose that the
incident beam, of unit amplitude, is linearly polarized normal to the plane of the
paper. We will call the amplitude of the refected wave b, and the amplitude of
the refracted wave ø. The refracted and reflected waves will, of course, be linearly
polarized, and the electric feld vectors of the incident, reflected, and refracted
waves are all parallel to each other. Pigure 33-6(b) shows the same situation, but
now we suppose that the incident wave, of unit amplitude, is polarized in the
plane of the paper. Now let us call the amplitude of the refected and refracted
wave Ö and A, respectively.
We wish 6o calculate how strong the refection is in the two situations illus-
trated in Fig. 33-6(a) and 33-6(b). We already know that when the angle bebtween
the relected beam and refracted beam is a right angle, there will be no reflected
wave in Fig. 33-6(b), but leb us see if we cannot get a quantitative answer——an
exact formula for Ö and ö as a function of the angle of incidence, ¿.
The principle that we must understand is as follows. The currents that are
generated in the glass produce two waves. First, they produce the reflected wave.
b —1 B —1
` a `v v \ A
_ _\*< |
1 Glass 1 Glass
(a) (@)
Fig. 33-6. An incident wave of unit amplitude ¡s reflected and refracted
at a glass surface. In (a) the incident wave is linearly polarized normal
to the plane of the paper. In (b) the incident wave is linearly polarized
In the direction shown by the dashed arrows.
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Moreover, we know that if there were no currents generated in the glass, the
incident wave would continue straight into the glass. Remember that all the
sources in the world make the net field. The source of the incident light beam
produces a field of unit amplitude, which would move into the glass along the
dotted line in the fgure. 'This field is not observed, and therefore the currents
generated in the glass must produce a fñeld of amplitude —1, which moves along