Lecture 12 - Polarization

DEVOTED TO 210-YEARS ANNIVERSARY OF KHARKIV NATIONAL MEDICAL UNIVERSITY
MINISTRY OF PUBLIC HEALTH OF UKRAINE
KHARKIV NATIONAL MEDICAL UNIVERSITY
DEPARTMENT OF MEDICAL AND BIOLOGICAL PHYSICS AND MEDICAL
INFORMATICS
MEDICAL AND BIOLOGICAL
PHYSICS
Lectures
KHARKIV - 2014
УДК 61:53+577.3](07.07)
ББК 28.901я7
М42
Approved by the Academic Council of Kharkiv National Medical University (minute N 5 at 22.05.2014)
Reviewers:
Berest V.P. - associate professor of Department of Molecular and Medical biophysics, PhD (Math.
and Physics), V. N. Karazin Kharkiv National University
Timanyuk V.O. - Chief of Department of Physics, professor, National University of Pharmacy
Authors:
Knigavko V.G., Zaytseva O.V., Batyuk L.V., Bondarenko M.A
M42 Medical and Biological Physics. Lectures (in 2 parts): Textbook for students
studying the subject in English: In 2 parts / Vladimir G. Knigavko, Olga V. Zaytseva, Lilia V. Batyuk,
Marina A. Bondarenko.-Kharkiv: Kh.N.M.U., 2014.; Part I - 337p., Part II - 254p.
The Textbook covers the most important topics of medical and biological physics in compliance with the typical
educational program. The structure and contents of the lectures completely correspond to credit-module system of
educational process organization.
The lectures are intended for teachers and students of the medical Universities, as well as for all interested in
medical and biological physics.
All rights reserved. No part of this publication may be reproduced in any material form (including photocopying or
storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this
publication) without the written permission of the publishers.
УДК 61:53+577.3](07.07)
ББК 28.901я7
© Kharkiv National Medical University, 2014
Kharkiv National Medical
University
POLARIZATION OF LIGHT
FUNDAMENTALS OF PHOTOMETRY
Department of medical and biological
physics and medical informatics
Light is known to propagate in the form of
electromagnetic waves. The human eye perceives
light wavelengths within the range of 380 nm to 760
nm.
An electromagnetic wave is the propagation of an
alternating electromagnetic field, the  direction of
oscillations of the electric intensity
vector ( E ) and of the

magnetic induction vector (B ) being perpendicular to
each other, and to the direction of wave propagation.
• One can assume that in a single act of radiation
the electron in the atom emits a light wave, in
which oscillation of vector E occurs in one
plane.
Ē
• Such a wave is called a plane-polarized one.
• The light wave emitted by a body as a whole, is
formed by addition of waves emitted by a multitude of
atoms with different orientation of vectors E chaotically
changing in time. Accordingly, the direction of
oscillation of vector E of the resulting wave changes.
• At this, all the directions of oscillation of the electric
intensity vector component are equivalent, and the
oscillation amplitudes are approximately equal. Such
light is called natural light or non-polarized light.
Natural light
• Therefore, all natural sources of light emit nonpolarized light. If the oscillation of vector occurs in
different directions perpendicular to the direction of
light propagation, but the amplitudes of oscillation in
some directions notably differ from that in other
directions, such light is called partially polarized
light.
Partially polarized light.
 

• The directions of oscillation of vector E in the plane ( E; B)
are shown in Fig. for the cases of natural (a), planepolarized (b) and partially polarized light (c) respectively.
• Let us randomly choose two mutually perpendicular planes,
passing through
a beam of ordinary light, and consider vector

projections E on them. Then the average value of these
projections will be the same. That is why it is convenient to
show ordinary light beam (unpolarized) as a straight line which
has equal number of both projections in the form of dashes and
dots (a). Thus, straight line with dots or dashes means a beam
of plane polarized light (b, c).
Natural (a)
Plane-polarized (b)
Partially polarized light (c)
 Light having both ordinary and polarized
components is called partially polarized. The beam
of partially polarized light is shown conventionally by
different
number
of
dots
and
dashes
(Fig. d), their relationship reflects a degree of
polarization.
a
c
b
d
Indication of natural (a), plane-polarized (b, c), and
partially polarized light (d)
• Polarizers are devices that extract polarized light
from natural light. Conversion of natural light to
completely or partially polarized light is called light
polarization.
• During incidence of natural light on a polarizer, the
intensity I p of polarized light, which exits the polarizer,
is one-half the intensity I n of natural light incident on
the polarizer.
In
Ip 
2
• If plane-polarized light obtained by means of one polarizer, is
incident on another polarizer, called an analyzer, the intensity of
light exiting the analyzer, is determined according to the Malus
law:
2
I  I 0  cos 
• where I is the intensity of light that has exited the analyzer; I0 is
the intensity of light incident on the analyzer (which has exited the
first polarizer); and φ is the angle between the plane of
polarization of incident light (the principal plane of the polarizer)
and the plane, in which the analyzer polarizes light (the principal
plane of the analyzer).
• It is obvious that, if φ = 0,I = I0 and φ = 90º. I = 0.
• Incidence of natural light on the interface of two
dielectrics is known to form reflected and refracted
rays. At this, in the general case, both of rays are
partially polarized, viz. the refracted ray is polarized
mainly in the incidence plane, and the reflected ray is
polarized in a plane, which is perpendicular to the
incidence plane.
• If the angle of incidence (αB) meets condition
tg  B  n
where n is the index of refraction of the second medium relative
to the first one, the reflected ray is completely polarized, and
the refracted ray is partially polarized, though the degree of its
polarization at this is maximum.
• The last relationship is called Brewster's law and the angle of
incidence, at which relation is fulfilled, is called Brewster's
angle.
• Thus, the boundary of two dielectrics or of a dielectric and
vacuum is a polarizer. To make the refracted ray completely
polarized, a set of thin transparent plates (the Stoletov’s
packet) is used.
• Partial polarization of the refracted ray occurs on every face of
every plate, due to which the degree of light polarization
increases, and in emerging from the pile, the light is almost
completely polarized.
αB
• Light polarization also occurs during double refraction (or
birefringence). The phenomenon of double refraction is
observed in an optically anisotropic media, i.e. in a media
whose optical characteristics depend on the direction of light
propagation therein.
• Typical examples of optically anisotropic media are crystals, for
example, Iceland spar. The velocity of light propagation in
optically anisotropic crystals differs in different directions. At
this, usually there is a direction in which the velocity of light
propagation is ultimate (i.e. either maximum, or minimum). This
direction is called the optical axis of a crystal.
• If a natural light ray is incident on an optically anisotropic crystal, due to
light refraction, two rays are formed in the general case
O‫׳‬
o
O
e
• The law of light refraction holds for one of these rays, i.e. the refracted
ray propagates in the plane of ray incidence, and such a ray is called the
ordinary ray (o).
• The other ray, which is called the extraordinary ray (e), propagates in
the plane formed by the incident ray and the crystal optical axis, which
passes through the point of ray incidence. This plane is called the
principal optical plane. Double refraction is not observed if the ray
propagates along the optical axis, and both beams (ordinary and
extraordinary) propagate with the same velocity.
• Both rays (the ordinary and extraordinary ones) are completely polarized,
the extraordinary ray being polarized in the principal plane, and the
ordinary ray being polarized in a plane perpendicular to the principal one.
• The propagation velocities of the ordinary and extraordinary
rays in an optically anisotropic medium are different. Hence, the
indices of refraction of the medium are different for these rays.
• Crystals, in which the propagation velocity of the ordinary ray
(vo) is greater than that of the extraordinary ray (ve), i.e. vo > ve,
are called positive crystals. If for a crystal vo < ve, such a
crystal is called a negative crystal.
• In some crystals with double refraction (tourmaline,
herapathite, and others), one of the rays is absorbed
more than others are. This phenomenon is called
dichroism. As a result, at sufficient thickness of a
crystal possessing dichroism property, only one
completely polarized ray exits there from. Such
crystals can be used as a light polarizers.
• To obtain achromatic polarized light, the Nicol prism
(or simply the nicol) can be used. The Nicol prism,
shown in Fig., is made of Iceland spar, and consists of
two parts whose edges are bonded with Canadian
balsam.
• The index of refraction of Canadian balsam (n = 1.55)
is greater than that of Iceland spar (n = 1.49) for the
extraordinary ray, but it is less than that of Iceland
spar (n = 1.66) for the ordinary ray.
• The prism is designed so that the angle of incidence of the
ordinary ray (о) on the interface of Iceland spar and Canadian
balsam is greater than the angle of total internal reflection.
• Due to this, the extraordinary ray passes through the bonded
edges of the prism and exits there from, and the ordinary ray
is totally reflected at the Iceland spar and Canadian balsam
interface. After this, the blackened side face of the prism
absorbs it. Hence, only a totally polarized extraordinary ray
exits the Nicol prism.
Canadian balsam
Natural light
Optically Active Substances
• There are substances, which are able to rotate the plane of light
polarization. Such substances are called optically active
substances.
• At this, the value of angle α is proportional to the length (l) of the path
over which the light has passed in the optically active substance, i.e.
where is a proportionality constant called rotation constant.
   0
where α0 is a proportionality constant called rotation constant.
Optically Active
Substances
α
l
• The specific rotation of a substance depends on the temperature and
the light wavelength. The dependence of specific rotation on the light
wavelength is the cause of rotation dispersion, i.e. the dependence
of the angle of rotation of the polarization plane on the light
wavelength.
• Solutions of optically active substances (for example, sugar) in
inert solvents (for example, water) are also optically active. For
such solutions, the angle of rotation of the plane of
polarization of light depends on the concentration of the
optically active substance. This dependence is described by
the formula
   0  c
• where c is the concentration of the optically active substance
in the solution, and [α0] is a proportionality constant called
specific rotation. The specific rotation of an optically active
substance solution depends on the wavelength, the solution
temperature, and the properties of the solvent.
• Dependence of [α0] on the wavelength λ is described by
the Biot law [α0]~1/λ2
• As evident, one can determine the concentrations of
an optically active substance in the solution by this
formula. This method of study is called polarimetry or
saccharimetry. The respective instruments are called
polarimeters or saccharimeters.
Polarizing Microscope
• The operation of a polarizing
microscope is based on light
polarization.
A
polarizing
microscope differs from an ordinary
(light field) one in that it contains a
polarizer and analyzer.
• The polarizer is placed before the
condenser and polarizes the light
that illuminates the object studied.
The analyzer is in the microscope
drawtube.
• If we have an isotropic sample
devoid of optical activity, and the
principal planes of the polarizer and
analyzer
are
mutually
perpendicular, the field of vision in
the polarizing microscope will be
dark. At this, either optically
anisotropic objects or optically
active ones can be observed in the
polarizing microscope.
• Tissues of living organisms contain various right-handed and lefthanded substances, the total optical activity of biologic tissues being
practically equal to zero. So the polarizing microscope is only used
for studying structures possessing optical anisotropy. Such structures
in the human organism are muscular, bone and neural tissues.
Polarization images of the muscular
(myocardium) (a), (b) and the large intestine
wall (c), (d) tissue histological sections.
FUNDAMENTALS OF PHOTOMETRY
• Photometry is the branch of optics that deals with the
measurement of energy transmitted by electromagnetic
waves of the optical range (of wavelengths from 10-8 to
3,410-3m). In the narrower sense, treated of below,
photometry refers to the branch of optics devoted to the
measurement of the effect of visible light on the human
eye (photometric measurements). This effect is
characterized by the following photometric quantities:
• luminous flux,
• luminous intensity,
• illumination,
• luminous emittance and luminance.
• The effect of visible light on the eye depends not only
on the physical characteristics of the light (energy flux
density, frequency or spectral composition), but also
on the spectral sensitivity of the eye (luminous
efficiency), which equals the ratio of the luminous flux
of the given monochromatic radiation to the energy
flux (radiant flux) of this radiation. The quantity
Ф
V 
(Ф  ) max
is called the relative spectral sensitivity of the eye
(or relative luminous efficiency).
• For a normal eye Vλ = 1 at λ = 5,55·10-7 m. For
light vision the dependence of Vλ on λ is called
luminous efficiency curve.
V(λ)
Λ, nm
• The luminous flux (Ф) is the power of visible
radiation evaluated according to its effect on the
eye.
• The luminous flux is measured in lumens.
• One lumen is luminous flux emitted within unit
solid angle Ω (one steradian) by a point source
having a uniform intensity of one candela. For
monochromatic radiation corresponding to maximum
luminous efficiency of radiation (λ = 5,55·10-7 m), the
luminous flux equals 683 lumens if the radiant power
is equal to 1 watt.
• The luminous flux across an arbitrary closed surface enveloping the
source of light, is equal to the power of visible radiation of the source
and is called the total luminous flux of the light source (Фtot). The
spectral density of visible radiation of a source of nonmonochromatic
radiation is the quantity
Ф е
dФ

d
where dФ is the total luminous flux for the wavelength range from λ to λ
+ dλ.
Ф

 v  k  V() e d
0
• The luminous intensity of a point source is the quantity I,
numerically equal to the luminous flux emitted by the source within a
unit solid angle. If the point source radiates uniformly in all directions
then its luminous intensity is:
Ф tot
I
4
where Фtot is the total luminous flux of the source.
• Luminous intensity is measured in candelas. The fundamental SI
unit is that of luminous intensity of a light source – the candela (cd) –
whose magnitude is such that the luminance of a full radiator (black
body) at the temperature of solidification of platinum is 60 candelas
per square centimeter.
• The illumination (E) of a surface is the ratio of the luminous flux dФ incident
on an element of the surface to its area dS. Thus:
dФ
Е
dS
• For a point source of light we get:
I cos 
E
R2
• where R is radians vector drawn from the source to the element dS of
illuminated surface; φ is an angle of incidence.
• If a plane light wave falls on the surface then we obtain
E  E 0 cos 
• where E0 is illumination of a surface normal to the direction of
propagation of the wave; φ is an angle between the normal
surface and that being considered.
• Illumination is measured in luxes and phots. One lux (lx) is
the illumination of the surface of a sphere of one meter
radius produced by a point source at its centre having a
luminous intensity of one candela. Nonsystem unit of
illumination is phot (ph): 1 ph = 104 lx.
• The quantity of illumination (exposure) H is the product of
illumination E of a surface by the duration t of its illumination (in
photography it is called the exposure time). Thus:
H = Et
• The luminance (Bφ) is the surface
density of the luminous intensity in a
given direction. It equals the ratio of the
luminous intensity to the projected area of
the luminous surface on a plane
perpendicular to the given direction. Thus:
d Ф
B 

dS  cos  dS  d  cos 
dI 
2
• where dI is a luminous intensity of element dS of the luminous
surface in the direction making the angle φ with the normal to
the element dS; d2Ф is luminous flux emitted by element dS
within solid angle dΩ in the same direction.
• The luminance is measured in nits and stilbs. One nit (nt) is
the luminance of a luminous plane surface in a direction
perpendicular to it, if in this direction the luminous intensity
equals one candela per square metre (1 nt = 1 cd/m2).
Nonsystem unit of luminance is stilb (sb): 1 sb = 104 nt.
• A light source for which Bφ does not depend on φ is said to be
obey Lambert’s law.
• The luminous emittance (R) is the surface density of the
luminous flux of radiation emitted by a surface. It equals
the ratio of the luminous flux dФ to the area dS of
luminous surface:
dФ
R
dS
• The luminous emittance is measured in luxes and
phots.
• The relationship between luminous emittance and
luminance for sources obeing Lambert’s law is
R  B
Thank You for Attention!
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