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Repetitorium in optics
Pavol Miškovský
Metódy optickej spektroskopie LS 2014
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Light as electromagnetic waves
Huygens was unconvinced by the particle theory of light advanced by Newton.
In 1687 he published a book „Traité de la Lumiere“, in which he suggested a
theory to explain the wave-like nature of light.
Huygens' theories neatly explained the laws of refraction, diffraction,
interference, and reflection
Maxwell unified the theories of electricity and magnetism. Electricity, magnetism and
light can now be understood as aspects of a single phenomenon: electromagnetic waves.
Using four equations, he described and quantified the relationships between
electricity, magnetism and the propagation of electromagnetic waves.
The equations are now known as Maxwell's Equations
In 1862 Maxwell wrote: "We can scarcely avoid the conclusion that light consists in the transverse
undulations of the same medium which is the cause of electric and magnetic phenomena."
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The term electromagnetic radiation, coined by Maxwell,
is derived from the characteristic electric and magnetic
properties common to all forms of wave-like energy.
Basic characteristics of electromagnetic waves
Light as transversal waves:
An electromagnetic wave travels or propagates in a direction that is oriented at right angles
to the vibrations of both the electric (E) and magnetic (H) oscillating field vectors, transporting
energy from the radiation source to an undetermined final destination. The two oscillating energy
fields are mutually perpendicular and vibrate in phase following the mathematical form of a sine
wave. Electric and magnetic field vectors are not only perpendicular to each other, but are also
T
T
perpendicular to the direction of wave propagation.
1
1
 2
I

S
dt

E dt
Light intensity:


T0
T0 
 . H   . E Poynting vector: S  E  H
Average energy pres unit area and per unit time
Transport of energy per unit time across a unit area
Plane harmonic electromagnetic wave: is wave for which the areas of equal phase are planes and which is periodic in time with
the periode T=1/n and in space with the period l
 
 
E r, t  E 0 r cos t  k r
aplitude

phase
The complex presentation
E  Re E  Re E 0 e
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ω angular frequency   2n
k is propagation number k  2 / l
it  k r
I 
3
1
2
*

1
EE 

2

E0

2
Full complex presentation of plane harmonic wave:
E  E 0e 
i t k r  0
  E 0 e i ei t k r   E c0 ei t k r 
0
Such wave is fully represented by polarization, frequency n [Hz], resp. energy E[eV],
wavelength l[nm] resp. wavenumber [cm-1], for which:
Quantum theory of light:
E  
Energy of photon
p   c
m0  0
Momentum of photon
mass of photon
group velocity (speed of energy propagation)
a phase velocity (speed of equivalent phase planes), for which:
v'  v  l
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dv
l dn 

 v 1 

dl
n
d
l


n ´n
for nondispersive media
4
  hn 
hc
l
hcl
VISIBLE LIGHT
Frequencies: 4 - 7.5 x 1014 Hz
Wavelengths: 750 - 400 nm
Quantum energies: 1.65 - 3.1 eV
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INFRARED LIGHT
WAVEFORMES OF LIGHT
Frequencies: 0.003 – 4x1014 Hz
Wavelengths: 1 mm - 750 nm
Quantum energies: 0.0012 - 1.65 eV
ULTRAVIOLET LIGHT
Frequencies: 7.5 x 1014 - 3 x 1016 Hz
Polychomatic vs. monochromatic
Wavelengths: 400 nm - 10 nm
E t  
Quantum energies: 3.1 - 124 eV
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
E
m  
6
m
exp im t 
Polarized light
Polarization is general property of all vector waves. For all these waves, polarization means a time behavior of one of vectors
associated with these waves observed in a defined place. For light this vector is the vector of electric-field vector E.
Thus, for light: light polarization is defined as the time development of the of electric-field vector in the plane perpendicular
to light propagation direction.
Description of light polarization
We can recognize three types of light polarization: elliptical, circular and linear
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Elliptical polarization
For the elliptically polarized light the end point of E will trace out an ellipse,
in a fixed-apace perpendicular to k (direction of light propagation)
Polarization is characterized by four parameters:

AZIMUT θ

2
 
Eb
Ea

2
e
AMPLITUDE A
A E E

ABSOLUTE PHASE δ
1  e  1
e  tg
ELLIPTICITY e
2
a
2
b

1
2


4
 

4
E a  A cos 
Eb  A sin 
    
Elliptically polarized wave = superposition of two lineary polarized and perpendicular waves with a phase shift    x   y
E x  E0 x cos t
E y  Eoy cost   
Ez  0
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 Ex

 Eox
2
Ey
  Ey 
  2 Ex
  
cos   sin 2 


Eox Eoy
  Eoy 
2
Equation of an ellipse for (Ex, Ey) - coordinate system
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Linear and circular polarization
Linear as well as circular polarizations may be considered
to be special cases of elliptically polarized light
The polarization type will depend on phase shift 
Depending on , the equation of the ellipse can be transormed
to an equation of a stragith line (linear polarization) and/or
circle (circular polarization)
Linear polarization: the phase shift of two linearly polarized and perpendicular components is
Ex
m E0 x
  1
   y   x  m
Ey
E0 y
Circular polarization: the phase shift of two linearly polarized and perpendicular components is
  y x  m

E0 y  E0 x  E
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2
E x2  E y2  E 2
Methods of polarized light generation
Polarized light may be generate from unpolarized (natural) light basically by:
reflection, refraction, absorption and scattering
Polarization by reflection
Reflection coefficients for waves polarized parallel
and perpendicular to the plane of incidence are different.
If the angle of incident light corresponds to that for which
the reflection coefficient for the parallel component is zero
(Brewster angle), the refracted light is linearly polarized
perpendicularly to the incident plane (Fresnel equations).
Polarization by bi-refraction (birefringence)
When light reflected from the pen is incident upon the surface of the Iceland
spar crystal (dichroic crystal), it is refracted into two wavefronts, polarized at
right angles to one another, and traveling at different velocities (optical anizotropy). This splitting of light is known as double refraction or birefringence
( bi-refraction).
One of the light waves, termed the ordinary ray travels
straight through the crystal (its image remains stationary),
while the other ray is refracted to a significant degree. The refracted ray
is termed the extra-ordinary ray.
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Polarization by absorption – dichroic polarizers
The polarizers illustrated in Figure 1 are actually filters containing long-chain polymer molecules that are oriented
in a single direction. Only the incident light that is vibrating in the same plane as the oriented polymer molecules
is passed through the first polarizing filter, while light vibrating at right angles to the polymer plane is absorbed.
The polarizing direction of the first polarizer is oriented vertically to the incident beam so it will pass only
the waves having vertical electric-field vectors. The wave passing through the first polarizer is subsequently
blocked by the second polarizer, because this polarizer is oriented horizontally with respect to the electric-field
vector in the light wave.
I  I 0cos 2 
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Speed of light
Light traveling in a uniform substance, or medium, propagates in a straight line at a relatively constant speed, unless it is refracted,
reflected, diffracted, or perturbed in some other manner. This well-established scientific fact is not a product of the Atomic Age or
even the Renaissance, but was originally promoted by the ancient Greek scholar, Euclid, somewhere around 350 BC in his
landmark treatise Optica.
When light traveling in a vacuum enters a new transparent medium, such as air, water, or
glass, the speed is reduced in proportion to the refractive index of the new material.
vacuum (n=1): 300 000 km/s, water (n=1.3): 225 000 km/s, glass (n=1.5): 200 000 km/s
diamond (n=2.4): 125 000 km/s
Roemer 1676 – Shortly after the invention of telescope, Danish astronomer Ole Roemer was the first
scientist to make a rigorous attempt to estimate the speed of light. By studying Jupiter's moon „Io“ and
its frequent eclipses, Roemer was able to predict the periodicity of an eclipse period for the moon and
calculate the speed of light v= 229 000 km/s
Recent measurements by the same method: v= 298 000 km/s
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Jean-Bernard-Leon Foucault (1862)
Albert Abraham Michelson 1878
Foucault developed a way to measure the speed of light
with extreme accuracy – method of rotating mirrors
(his doctoral thesis)
c  8ad b 298000km/ s
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Determined speed of light by more sophisticated
Method of rotating mirrors: 299 909 km/s
Finally in 1983, more than 300 years after the first serious measurement attempt,
the speed of light was defined as being 299,792.458 kilometers per second by the
Seventeenth General Congress on Weights and Measures.
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Estimate
Kilometers/Second
Date
Investigator
Method
1667
Galileo Galilei
Covered Lanterns
333.5
1676
Ole Roemer
Jupiter's Moons
220,000
1726
James Bradley
Stellar Aberration
301,000
1834
Charles Wheatstone
Rotating Mirror
402,336
1838
François Arago
Rotating Mirror
1849
Armand Fizeau
Rotating Wheel
315,000
1862
Leon Foucault
Rotating Mirror
298,000
1868
James Clerk Maxwell
Theoretical Calculations
284,000
1875
Marie-Alfred Cornu
Rotating Mirror
299,990
1879
Albert Michelson
Rotating Mirror
299,910
1888
Heinrich Rudolf Hertz
Electromagnetic Radiation
300,000
1889
Edward Bennett Rosa
Electrical Measurements
300,000
1890s
Henry Rowland
Spectroscopy
301,800
1907
Edward Bennett Rosa and Noah Dorsey
Electrical Measurements
299,788
1923
Andre Mercier
Electrical Measurements
299,795
1926
Albert Michelson
Rotating Mirror (Interferometer)
299,798
1928
August Karolus and Otto Mittelstaedt
Kerr Cell Shutter
299,778
1932 to 1935
Michelson and Pease
Rotating Mirror (Interferometer)
299,774
1947
Louis Essen
Cavity Resonator
299,792
1949
Carl I. Aslakson
Shoran Radar
299,792.4
1951
Keith Davy Froome
Radio Interferometer
299,792.75
1973
Kenneth M. Evenson
Laser
299,792.457
1978
Peter Woods and Colleagues
Laser
299,792.4588
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Light: Particle or a Wave? Duality of light, particle-like and/or wave-like behavior.
The exact nature of visible light is a mystery that has puzzled man for centuries. In the early eighteenth century, the argument about
the nature of light had turned the scientific community into divided camps that fought vigorously over the validity of their favorite theories.
One group of scientists, who subscribed to the wave theory, centered their arguments on the discoveries of Christiaan Huygens.
The opposing camp cited Sir Isaac Newton's experiments as proof that light traveled as a shower of particles, each proceeding in
a straight line until it was refracted, absorbed, reflected, diffracted or disturbed in some other manner.
Only during the first decades of the twentieth century was enough compelling evidence collected to provide a comprehensive answer,
and to everyone's surprise, both theories turned out to be correct, at least in part
duality of light
Refraction of light – Huygens' theory
Support for wave theory
WT: velocity of light in any substance is inversely proportion
to its refractive index – velocity decreasing
PT: additional force which cause the refraction – velocity increasing
200 years of fight based on
supporting experiments:
Reflection of light
•Refraction
•Reflection
•Difraction
•Polarization
•Photoelectric phenomena
•Compton scattering
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Support for particle theory
Both the particle and wave theories adequately explain reflection from a smooth
surface. However, the particle theory also suggests that if the surface is very rough,
the particles bounce away at a variety of angles, scattering the light.
This theory fits very closely to experimental observation.
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Diffraction of particles and waves
Thomas Young 1801
Newton 1704 (Opticks): "Light is never known to follow crooked
passages nor to bend into the shadow". This concept is consistent
with the particle theory, which proposes that light particles must
always travel in straight lines.
Like waves in water, light waves encountering the edge of
an object appear to bend around the edge and into its
geometric shadow, which is a region that is not directly
illuminated by the light beam.
Young believed that light was composed of waves. He used a screen containing a
single, narrow slit to produce a coherent light beam (containing waves that propagate
in phase) from ordinary sunlight. When the sun's rays encounter the slit, they spread
out or diffract to produce a single wavefront. If this front is allowed to illuminate a
second screen having two closely spaced slits, two additional sources of coherent
light, perfectly in step with each other are produced and interfere.
Young postulated that light of different colors was composed of waves having
different lengths, a fundamental concept that is widely accepted today. In contrast,
the particle theory advocates envisioned that various colors were derived from
particles having either different masses or traveling at different speeds.
Polarization
Support for wave theory
If a beam of light is allowed
to impact a polarizer, only
light rays oriented parallel
to the polarizing direction
are able to pass through
the polarizer.
Support for wave theory
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Strong support for wave theory
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The effect is easily explained with the wave theory, but
no manipulation of the particle theory can explain how
light is blocked by the second polarizer.
By the middle of the 19th century, scientists were becoming increasingly convinced of the wave-like character of light.
James Clerk Maxwell: all forms of electromagnetic radiation represent a continuous spectrum, and travel through a vacuum at the same
speed: 186,000 miles per second (Maxwell's calculation) . Maxwell's discovery effectively nailed the coffin of the particle theory.
It seemed that the basic questions of light and optical theory had finally been answered.
A major blow to the wave theory = photoelectric effect ( Philipp Lenard 1880)
Lenard used a prism to split white light into its component colors, and then selectively focused each color
onto a metal plate to expel electrons. Electrons escaping their atomic bonds had energies that were
dependent on the wavelength of light, not the intensity. This is contrary to what would be expected from
the wave theory. Lenard also discovered a link between wavelength and energy: shorter wavelengths
produced electrons having greater amounts of energy.
Max Planck 1900:
Planck ad hoc proposed that radiation energy can exists as discrete entities
which are proportional to light frequency
Black body radiation
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E  hn
17
= quantum = photon
E  mc2
Albert Einstein ~ 1905
In 1905, Albert Einstein postulated (on the basis of Planck theory) that light might actually have some particle
characteristics, regardless of the evidence for a wave-like nature. In developing his quantum theory, Einstein
suggested mathematically that electrons attached to atoms in a metal can absorb a specific quantity of light (first
termed a quantum, but later changed to a photon) and thus have the energy to escape.
Arthur H. Compton ~ 1920
Luis-Victor de Brolie
Einstein's theory was solidified in the 1920s by the experiments
of American physicist Arthur H. Compton, who demonstrated
that photons had momentum, a necessary requisite to support
the theory that matter and energy are interchangeable.
Louis-Victor de Broglie proposed that all matter and radiation have
properties that resemble both a particle and a wave. De Broglie,
following Max Planck's lead, extrapolated Einstein's famous formula
relating mass and energy to include Planck's constant:
E = mc2 = hn
Duality of light – conclussion:
De Broglie's work, which relates the frequency of a wave to the energy and mass of
a particle, was fundamental in the development of a new field that would ultimately
be utilized to explain both the wave-like and particle-like nature of light.
At times light behaves as a particle, and at other times as a wave.
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THE PROPAGATION OF LIGHT
Reflection and Refraction
Interference
Diffraction
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Reflection and Refraction of light
Refraction of light
When electromagnetic radiation, in
the form of visible light, travels from one
substance or medium into another,
Reflection of light (and other forms of electromagnetic radiation) occurs when
the waves encounter a surface or other boundary that does not absorb the energy the light waves may undergo a phenomenon known as refraction, which is
of the radiation and bounces the waves away from the surface. The simplest
example of visible light reflection is the surface of a smooth pool of water, where manifested by a bending or change in direction of the light. Refraction occurs
as light passes from one medium to another only when there is a difference
incident light is reflected in an orderly manner to produce a clear image of
in the index of refraction between the two materials
the scenery surrounding the pool.
Reflection of light
The history of the refraction of light is younger
Ptolemaios – As early as the first century Ptolemy attempted to
mathematically explain the amount of bending (or refraction) light
Willebroad Snell (17th cent.): succeeded in developing a law that defined
a value related to the ratio of the incident and refracted angles, which has
subsequently been termed the bending power or refractive index of a
substance. Snell never discovered the reason for this refraction effect.
Some of the earliest accounts of light reflection originate from the ancient
Greek Euclid, who conducted a series of experiments around 300 BC, and
appears to have had a good understanding of how light is reflected. However,
it wasn't until a millennium and a half later that the Arab scientist Alhazen
proposed a law describing exactly what happens to a light ray when it strikes
a smooth surface and then bounces off into space.
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Christian Huygens (1678) devised a mathematical relationship to explain
Snell's observations and proposed that the refractive index of a material is
related to the speed at which light travels through the substance. (n=c/v)
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As in the life, everything can be simple and/or complicated. But more deeply we go, more interesting and challenging the life is!
The same rule you can find in physics (optics). More deeply we explore the processes of reflection, refraction and scattering, the more challenging they become.
Beyond that many fascinating questions need to be address: How does light move trough a material medium? What happens to it as it does?
What light appears to travel at the speed other than c when photons can only exist at c?T
Mathematical description of reflection and refraction of light – Fresnell relations (1823)
Problem: found association between amplitudes of incident, reflected and refracted waves - Fresnell relations
Incident light
Schema of arrangement
Components of the electric-field-vector
A – amplitude of incident light
T – amplitude of refracted light
R – amplitude of reflected light
E x( i )   AII cos  i e  i i
E y( i )   A e i i
because
H 
E z( i )   AII sin  i e  i i
H x(i )   A cos i

r.s ( i )
 i    t 
v1

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

x sin  i  z cos  i





t 
v1


H y( i )   AII




 1 e  i
H z( i )  A sin i
21
1 e i
i
1 e i
i
i
 sE
Boundary conditions: tangential components of field vectors
Must be continuous, thus:
E x(i )  E x( r )  E x(t )
E y( i )  E y( r )  E y( t )
H x(i )  H x( r )  H x(t )
H y( i )  H y( r )  H y( t )
In using relations:
Fresnel equations
1823
cosr = cos( - i) = - cosi
cos  i ( AII  RII )  cos  t TII
 1 ( AII  RII ) 
n
TII 
T 
 2 TII

2n1 cos  i
n2 cos  i  n1 cos 
AII
t
2 sin  t cos  i
AII
sin(  i   t ) cos( i   t )
T 
2 sin  t cos  i
A
sin(  i   t )
RII 
tan( i   t )
AII
tan( i   t )
sin(  i   t )
A
sin(  i   t )
 2 cos  t T
Independent perpendicular
and parallel components
Fresnel equations
2n1 cos  i
A
n1 cos  i  n2 cos  t
RII 
n2 cos  i  n1 cos  t
AII
n2 cos  i  n1 cos  t
R 
n1 cos  i  n2 cos  t
A
n1 cos  i  n2 cos  t
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 2 2
n
 2  n12
11
n1
TII 
R  
A  R  T
 1 cos  i ( A  R ) 
sin  i
v
 1 
sin  t
v2
 i   t  90 0
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Simple way – Laws of reflection and refraction derived from the Principle of Fermat
Fermat´s principle
„The actual path between two points taken by a beam of light is the one that is traversed in the least time“
Laws of reflection derived from the Principle of Fermat
The length of path from point A to point B
We are looking a minimal time for light path the distance from A to B
(minimal time is for minimal path)
x
a x
2
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2

(d  x)
b  (d  x)
2
2
what is
sin  i  sin  r
i   r
Laws of refraction derived from the Principle of Fermat
The same approach as for reflection. Light path from the point A to the point B in time t.
We are looking a minimal time for light path the distance from A to B
School of biophotonics Kosice June 2013
24
Brewster Angle derived from the Snell´s law
David Brewster 1781-1868
 i  arctg
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nt
ni
Practical applications of Laws of reflection and refraction – geometrical optics
Figure generated by a lens can be constructed in using just 3 principal rays
•
•
•
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Ray parallel to the optical axis will project trough focal point
Ray going trough the lens center is not decline
Ray going trough the focal point wil project parallel to optical axis
26
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Mirrors
Image created by concave mirror – real image
Ray diagram is the same as for lenses
(the same principal rays)
Real inverted
Image created by convex mirror – virtual image
Real direct
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Interference of Light Waves
The formation of an image in the microscope relies on a complex
interplay between two critical optical phenomena:
diffraction and interference.
Examples of interference
Morpho didius butterfly (Amazon rain forest)
The dynamic interplay of colors in a soap bubble derives
from simultaneous reflection of light from both the inside
and outside surfaces of the exceedingly thin soap film.
The two surfaces are very close together (separated by
only a few micrometers) and light reflected from the inner
surface interferes both constructively and
destructively with light reflected from the outer surface.
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The intense blue wing color is the consequence
of color-producing structures fastened to
the scales layering the butterfly's wings. Plates
on the ridges arising from thin layers of chitin that are separated by air spaces at distances
equal to one-half the wavelength of blue light mimic a natural diffraction grating.
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  2 l S
Interference on thin plan-parallel layer
 
4
l0
n , h cos  '
Because the reflection changes the phase by , the resulting difference
in phase is :

4
l0
n , h cos  '   
4h
l0
n , 2  n 2 sin 2   
In using realtions for intereference extrems
Calculate the phase shift
Because we are looking for interference, we have to calculate
the path difference between 2 rays which creates the phase
difference = interference
I  I1  I 2  2 I1 I 2 cos 
  0,2 ,4 ,...
I min  I1  I 2  2 I1I 2
S  n ,  AB  BC   nAN
See just geometry
h
AB  BC 
cos  '
AN  AC sin   2htg ' sin 
n ' sin  '  n sin 
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S  2n , h cos  '
and substitute
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   ,3 ,5 ....
Thomas Young's Double Slit Experiment
Thomas Young 1801
We need to calculate the phase difference between these rays
2
s1  S1 P 
d

a2  y2   x  
2

s2  S 2 P 
d

a2  y2   x  
2

because
s22  s12  2 xd
2
s2  s1  2a
s 
thus connected phase difference
interference max and min are expressed by I
Physical description of Young´s experiment
School of biophotonics Kosice June 2013
 
nxd
a
2 nxd
l0 a
 I1  I 2  2 I1 I 2 cos 
´distance between interf. max
x
malo
,
nd
´distance between interf. min
x
malo
nd
31
2 xd
s2  s1
xd
a
S  n s 
considering refraction index
Demonstration of the wave-like character of light through
the phenomenon of interference using diffraction techniques.
s  s2  s1 
for
for
m  0,1,2,...
m 
1 3 5
, , ...
2 2 2
Diffraction
Diffraction of the light occurs when a light wave passes
very close to the edge of an object or through a tiny opening,
such as a slit or aperture. The light that passes through the
opening is partially redirected due to an interaction with
the edges.
When the wavelength exceeds the size of the slit, diffraction of the light occurs,
causing the formation of a diffraction pattern consisting of a bright central
portion (the primary maximum), bounded on either side by a series of
secondary maxima separated by dark regions (minima). The maxima and
minima are created by interference of diffracted light waves.
For l > d,
diffraction is
observed
sin   ml
The terms diffraction and scattering are often used interchangeably
and are considered to be almost synonymous in many cases.
Diffraction describes a specialized case of light scattering in which
an object with regularly repeating features (such as a periodic
objector a diffraction grating) produces an orderly diffraction pattern
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d
Diffraction is a limited factor for optical resolution
Because the image-forming light rays are diffracted, a single
point of light is never really seen as a point in the microscope,
but rather as a diffraction pattern containing a central disk or
spot of light having a finite diameter and encircled by a fading
series of rings.
The central diffraction spot or disk is called an Airy disk, (Sir George Airy).
The Airy disk pattern is a direct result of diffraction, and demonstrates
the alteration of points of light that make up an image using an optical
instrumentsuch as a microscope.
Experimentally, resolution can be increased by decreasing the wavelength of
light utilized to image the specimen (from white light to blue, for example) or by
increasing the numerical aperture of the objective and condenser combination
The radius of the diffraction spot (r) for a point of light in
the image plane is given by the related expression:
r  1.22  l
Rayleigh´s criterion
2 NA
Two maxima of the same intensity can be resolved up to the limit for which,
the maximum of the firts one is in the position of the minimum of the second one
D  r  0.61 l
the numerical aperture (NA) of a microscope objective is defined as
NA  n  sin 
 is half angle aperture
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NA
Interaction of light with bio-matter
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Microwaves radiation
Atmosferické oblasti absorpcie a priepustnosti
elektromagnetického žiarenia
microwave
(n=2.25 GHz resp. l=12.2 cm) – water absorption
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Infrared radiation
Green house effect
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Visible radiation
Absorption by skin
0.4 až 0.7 mm (energie 1.6 – 3.2 eV)
Absorption a) and fluorescence b) by pigments of human skin
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Ultraviolet radiation
400 až 10 nm (energie 3.1 – 124 eV)
Absorption a) and fluorescence b) by pigments of human skin
Autofluorescence of cancer tissue
Hypericin fluorescence in vessels
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RTG radiation
Physiological effects of electromagnetic radiation on human body
Wavelengths < 10 nm (energies > 124 eV)
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How does light move trough a material medium?
What happens to it as it does?
Interaction of light with matter
sample
Source of light
IA
IR
IT
ISC
Maxwell´s equations in material medium
Material medium is characterized by:
•permittivity ε
•permeability μ
Used model:
•linear optics
•we do not consider magnetic field interaction with matter (μr=1)
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rot H  j 
D
t
div D  r
rot E  
B
t
div B  0
P  0 E E
- E electric-field vector
- H magnetic field vector
- D electric induction vector
- B magnetic induction vector
- j current density vector
- r density of free charges
j 
M  0  M H

E
electric susceptibility
M
magnetic susceptibility
 
E
conductivity
 
   0 1   E   0  r   0 1   M  0 r
r
D  0 E  P
r
B  0 H  M
0
permittivity of vacuum
B  H
 0 permeability of vacuum
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relative permittivity
relative permeability
41
D E
H
t
E
rot H  
t
rot E   
div E  0
div H  0
v
2 E
 E   2  0
t
wave equation
1

   0 r
and because
  0 r
vc n
v
1


1
 0  0 r  r
n
 r r
What about next steps ? 1. Absorption (complex space) 2. Dispersion ()
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
c
 r r

c
n
n
r
2
2
N
e
f



0i
 r1  n 2  K A2  1   0i i i
mi 0 02i   2 2  gi 2 2
i
2


N 0i ei f i
g i
 r 2  2nK A  
2
2 2
m

i
0i    gi 2 2
i 0
2

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
43
Energy
Jablonsky diagram
F=
S2
Internal conversion
kic
 F=
hnF
hnA
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Absorption
Fluorescence
Lifetime of fluorescence
[Q]
kQ
Intersystem conversion
kisc
kF
2
1
0
Quantum yield of fluorescence
1
1
=
kF
kF+[Q].kQ+ki
S1
F
kF
ki
kic
T1
kp
hnP
Phosphorescence
44
44
Resources:
1.Eugen Hecht: OPTICS, 4th edition, Addison Wesley 2002
2.Max Born & Emil Wolf: Principles of optics, Pergamon press,1964
Thank you for your attention
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