Nature and Propagation of
Light
1000 Years of Arabic Optics to be a Focus
of the International Year of Light in 2015
On 20 December 2013, The United Nations
General Assembly proclaimed 2015 as
the International Year of Light and Lightbased Technologies (IYL 2015).
Aimed at raising global awareness of how
light-based technologies can provide
solutions to global challenges in energy,
education, agriculture and health, this
UNESCO-led initiative will also be an
opportunity to celebrate the work of the
10th century scientist Ibn Al-Haytham.
Ibn Al-Haytham
• Ibn Al-Haytham was a pioneering polymath from Basra (in
modern-day Iraq) who lived in the 10th century and is often
referred to as the ‘father of modern optics’. He made
significant advancements in optics, mathematics and
astronomy, and helped lay the foundations of the present day
scientific experimental method.
• “I am pleased to partner with the International Organisation
1001 Inventions to launch the World of Ibn Al Haytham Global
Campaign, to promote light-science for the benefit of all,” said
UNESCO Director-General Irina Bokova “A ground-breaking
scientist and a humanist from a thousand years ago, the life
and work of Ibn Al-Haytham have never been as relevant as
they are today.”
• Following the January launch, the campaign will roll out in
countries around the world.
• Other initiatives to celebrate Ibn Al-Haytham include
educational actions coordinated by a high-level Ibn-Al
Haytham Working Group, and a dedicated conference an
exhibition at UNESCO HQ starting on 14 September 2015
entitled The Islamic Golden Age of Science for the KnowledgeBased Society.
• This conference will see experts in science, history and culture
engage world leaders and the public with fascinating insights
into the era of ground-breaking discoveries and innovations by
scientists of different cultures and faiths who lived during that
period of Muslim Civilization over 1,000 years ago.
• This International Year has been the initiative of a large range
of scientific bodies together with UNESCO, and will bring
together many different stakeholders including scientific
societies and unions, educational institutions, technology
platforms, non-profit organizations and private sector partners.
• The life and works of Ibn-Al Haytham will be the subject of
several major initiatives during 2015.
• Beginning at the Opening Ceremony of the International Year
on 19 January 2015 at UNESCO HQ in Paris.
• The Ceremony will see the launch of 1001 Inventions and the
World of Ibn Al-Haytham, a global campaign where UNESCO
will partner with the science and cultural heritage
organization 1001 Inventions to announce a series of
interactive exhibits, workshops and live shows illustrating the
world of this remarkable scientist.
IYL-2015 will commemorate the achievements of
scientific figureheads, who paved the way ahead for
humanity’s understanding of light:
1015 – Ibn Al-Haytham’s Book of Optics;
1815 – Augustin-Jean Fresnel and the wave nature of light;
1865 – James Clerk Maxwell and electromagnetic waves;
1915 – Einstein’s theory of general relativity, exploring light
through space and time;
1965 – Arno Penzias and Robert Wilson’s discovery of cosmic
microwave background, and Charles Kao’s pioneering
development of fiber optics, which enabled
transformative technologies such as broadband today.
Some Contributions of Ibn Al-Haytham
(Alhazen)
• Alhazen's most famous work is his seven-volume treatise on
Kitab al-Manazir (Book of Optics), written from 1011 to 1021.
• The book was translated into Latin at the end of the 12th
century or the beginning of the 13th century. It was printed by
Friedrich Risner in 1572, with the title Opticae thesaurus:
Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber
De Crepusculis et nubium ascensionibus (English : Optics
treasure: Arab Alhazeni seven books, published for the first
time: The book of the Twilight of the clouds and ascensions).
• Risner is also the author of the name variant "Alhazen”. This
work enjoyed a great reputation during the Middle Ages.
• Works by Alhazen on geometric subjects were discovered in
the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot.
• Other manuscripts are preserved in the Bodleian
Library at Oxford and in the library of Leiden.
• It is Alhazen's work which contains the first clear
description pin hole camera (camera obscura) and early
analysis of the device.
• On the Configuration of the World, Alhazen presented a
detailed description of the physical structure of the earth.
• Alhazen's The Model of the Motions of Each of the Seven
Planets was written in 1038.
• According to medieval biographers, Alhazen wrote more than
200 works on a wide range of subjects, of which at least 96 of
his scientific works are known.
• Most of his works are now lost, but more than 50 of them
have survived to some extent.
Nearly half of his surviving works are on mathematics, 23 of them are on
astronomy, and 14 of them are on optics, with a few on other subjects.
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Book on Optics
Analysis and Synthesis
Balance of Wisdom
Corrections to the Almagest
Discourse on Place
Exact Determination of the Pole
Exact Determination of the Meridian
Finding the Direction of Qibla by
Calculation
Horizontal Sundials
Hour Lines
Doubts Concerning Ptolemy
Maqala fi'l-Qarastun
On Completion of the Conics
On Seeing the Stars
On Squaring the Circle
On the Burning Sphere
On the Configuration of the World
On the Form of Eclipse
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On the Light of Stars
On the Light of the Moon
On the Milky Way
On the Nature of Shadows
On the Rainbow and Halo
Opuscula
Resolution of Doubts Concerning the
Almagest
Resolution of Doubts Concerning the
Winding Motion
The Correction of the Operations in
Astronomy
The Different Heights of the Planets
The Direction of Mecca
The Model of the Motions of Each of the
Seven Planets
The Model of the Universe
The Motion of the Moon
The Ratios of Hourly Arcs to their Heights
The Winding Motion
Treatise on Light
Treatise on Place
Treatise on the Influence of Melodies on
the Souls of Animals[115]
Light
• In the fifth century BC, the Greek philosophers determined the link
between the eye and the object seen.
• The linked could be thought to be ‘something’ which was emitted
by the eye and traveled to the object, or ‘something’, which
traveled towards the eye from the object, or the co-existence of
both ‘something’ traveling in the opposite directions.
• Abu Yosuf Yaqub Ibn Is-haq (known as Alkindi in the west) dealt very
explicitly with the problems of optics. He asserted that vision had to
take place by means of rays capable of having a physical action
upon the eye.
• Alkindi transformed and perfected the idea of a ray.
• He noted that the formation of shadows produced by bodies when
illuminated by lumina which entered from a window, led without
any doubt to the conclusion that the rays emanating from luminous
bodies traveled along rectilinear paths
• After Alkindi, the prominent Muslim philosopher was Abu Ali
Mohammed Ibn Al Hasan Ibn Al Haytham (known as Alhazan), who
made the long lasting effect in all the sciences especially in the field
of medicine and optics.
• The translation of one of his book, Opticae Thesaurus libri septem,
per Episcopios, earned a great respect in the west and was taught
for many centuries.
• Alhazan accepted the theory of Alkindi about light and elaborated it
with fine details. Alhazan’s results were supported by experiments;
he proved that by looking at the sun or its reflection through a
mirror produced pain in the eye.
• This clearly shows that if there were something, which travels from
the eye to the object, then there would be no reason to feel pain.
• Similarly he proved the persistence of the image on the ratina.
• In his theory of light, Alhazan attributed to this light the property of
reflection when it met a mirror, and of refraction when it traveled
through transparent surfaces.
• He gave full reasoning of the reflection and refraction.
Nature of Light
• Light is an elephant
An old story tells of three blind men who were asked to
describe an elephant.
• One blind man touched the elephant’s tail and said
the elephant was long and thin like a rope.
• The second blind man touched the elephant’s leg
and described the elephant as round and hard like a
tree trunk.
• The third man felt an ear and said that the elephant
was thin and flat, like a huge leaf.
Each man’s description was correct, but didn’t give the
complete picture.
• Scientists who study the nature of light are like
the blind men in the story.
• They try to describe light, but their descriptions
depend very much on which aspects of light
they study.
• Each description of light is merely an
approximation to the reality that is light.
• During the last four centuries, light is sometimes
considered as particle and sometimes as wave,
now scientists agreed on its dual nature.
• Wave theory of Huygens (1629-1695) described the light as
waves like water or sound waves.
– The theory not only satisfied the diffraction, interference
and polarization but also explained the reflection and
refraction of light.
– The theory assumed some medium (ether) in space to
propagate light waves from the sun.
• Corpuscular theory of Newton (1643-1727) described that
light rays consisted of streams of tiny particles, which are
emitted by the light sources and propagate through space in
straight lines.
– The theory satisfied the phenomena of reflection and
refraction and received a general acceptance in the
seventeenth century. But it failed to explain the
phenomena like diffraction and interference.
• Maxwell (1831-1879) combined the laws of
electricity and magnetism and proposed the
electromagnetic nature of light, which do not require
a medium to travel.
• The theory satisfied all the problems faced till the
end of nineteenth century and received such a
universal acceptance that scientists believed that
problem regarding the nature of light had been
solved and the corpuscular theory was
comprehensively rejected.
• The experimental phenomenon of photoelectric
effect and the blackbody radiation introduced the
quantum theory of light and gave rebirth to the
particle nature.
The Nature of Wave (what’s waving?)
•propagation of a light wave does NOT require a medium
•Light can propagate through empty space (vacuum)
Consider two of MAXWELL’S EQUATIONS OF
ELECTROMAGNETISM:
B
 E 
t
E
  B  0 J  0 0
t
(essentially Faraday’s law and Ampere’s law, respectively)
Electromagnetic Waves
After some mathematical manipulation we find that the
electric and magnetic fields obey the WAVE
EQUATIONS:
 Ey
2
x
2
 0 0
 2 y ( x, t )
x 2
 Ey
2
t 2
1  2 y ( x, t )
 2
v
t 2
“standard” linear wave equation
 2 Bz
 2 Bz
 0 0 2
2
x
t
c
1
 0 0
Electromagnetic Waves
Energy in Electromagnetic Waves
•For a wave, intensity = energy flow through unit area per
unit time = P/A
•In the case of an EM wave, intensity corresponds to the
“brightness” of the radiation
c 0 2
I
E0
2
•Studies of the PHOTOELECTRIC EFFECT by Lennard
(~1900) gave results that could not be explained by the
classical wave picture of light………
The simplest waves are
sinusoidal waves, which can be
expressed mathematically by the
equation:
E
Eo
𝐸 𝑥, 𝑡 = 𝐸0 . cos(𝜔𝑡 − 𝑘𝑥 + 𝜑)
E
x
-Eo

(a)
Eo
t
-E

where 𝐸 𝑥, 𝑡 is the value of the
electric field at the point x at
(b)
time t.
Figure 1.2 The electric field (E) of an electromagnetic wave plotted as a
o
function of (a) the spatial coordinate x and (b) the time t.
The electromagnetic spectrum (Light)
-It is a form of energy, which can be transmitted from one place
to another at a finite velocity.
-Visible light is a small portion of a continuous spectrum of
radiation ranging from Gamma rays to radio waves.
Gamma rays (3x10-9m) → Radio waves (3x106m)
Nature of electromagnetic radiation
• Requires no supporting media
• Uniform velocity in vacuum (2.9979 x 108 m s-1)
Two complimentary theories have been proposed to explain
how light behaves and the form by which it travels.
•Photons or waves?
Particle Theory (Photons)
- release of a small amount of energy as a photon when an atom
is excited.
• Discontinuous ‘packets’ or quanta of energy
• Defined by Planck's constant (h) = 6.63×10-34 J·sec
• Photons best explain some aspects of shortwave
radiation behaviour
Wave Theory
- radiant energy travels as a wave from one point to
another.
-Wave theory effectively describes the phenomena of
polarization, reflection, refraction and interference, which form
the basis for optical mineralogy.
-Waves best explain some aspects of long wave
radiation behaviour
• Plane waves of energy
•Waves have electrical and magnetic properties =>
electromagnetic variations.
(Electric and magnetic fields at right angles)
Waves
The electric and magnetic components vibrate at right angles to
each other and at right angles to the direction of propogation
Measurements of the Speed of Light
•Since light travels at a very high speed, early
attempts to measure its speed were
unsuccessful.
– Remember c = 3.00 x 108 m/s
•Galileo tried by using two observers separated
by about 10 km.
– The reaction time of the observers was more than
the transit time of the light.
Measurement of the Speed of Light
– Rømer’s Method
•In 1675 Ole Roemer used
astronomical observations to
estimate the speed of light.
•He used the period of
revolution of Io, a moon of
Jupiter, as Jupiter revolved
around the sun.
•The angle through which
Jupiter moves during a 90°
movement of the Earth was
calculated.
Roemer’s Method…
•The periods of revolution were longer when the
Earth was receding from Jupiter.
– Shorter when the Earth was approaching
•Using Roemer’s data, Huygens estimated the
lower limit of the speed of light to be 2.3 x 108
m/s.
– This was important because it demonstrated that
light has a finite speed as well as giving an
estimate of that speed.
Measurements of the Speed of Light –
Fizeau’s Method
•This was the first successful method for
measuring the speed of light by means of a
purely terrestrial technique.
•It was developed in 1849 by Armand Fizeau.
•He used a rotating toothed wheel.
•The distance between the wheel and a mirror
was known.
Fizeau’s Method…
•d is the distance
between the wheel
and the mirror.
•Δt is the time for one
round trip.
•Then c = 2d / Δt
•Fizeau found a value
of
c = 3.1 x 108 m/s.
Reflection of Light
•A ray of light, the incident ray, travels in a medium.
•When it encounters a boundary with a second
medium, part of the incident ray is reflected back
into the first medium.
– This means it is directed backward into the first
medium.
•For light waves traveling in three-dimensional
space, the reflected light can be in directions
different from the direction of the incident rays.
Specular Reflection
•Specular reflection is
reflection from a
smooth surface.
•The reflected rays are
parallel to each other.
Diffuse Reflection
•Diffuse reflection is
reflection from a rough
surface.
•The reflected rays travel
in a variety of directions.
•A surface behaves as a
smooth surface as long as
the surface variations are
much smaller than the
wavelength of the light.
Law of Reflection
•The normal is a line
perpendicular to the
surface.
– It is at the point where
the incident ray strikes
the surface.
•The incident ray makes
an angle of θ1 with the
normal.
•The reflected ray makes
an angle of θ1’ with the
normal.
Law of Reflection…
•The angle of reflection is equal to the angle of
incidence.
θ1’= θ1
– This relationship is called the Law of Reflection.
•The incident ray, the reflected ray and the
normal are all in the same plane.
Multiple Reflections
•The incident ray strikes the
first mirror.
•The reflected ray is directed
toward the second mirror.
•There is a second reflection
from the second mirror.
•Apply the Law of Reflection
and some geometry to
determine information
about the rays.
Retroreflection
•Assume the angle between two mirrors is 90o .
•The reflected beam returns to the source
parallel to its original path.
•This phenomenon is called retroreflection.
•Applications include:
– Measuring the distance to the Moon
– Automobile taillights
– Traffic signs
Refraction of Light
•When a ray of light traveling through a
transparent medium encounters a boundary
leading into another transparent medium, part
of the energy is reflected and part enters the
second medium.
•The ray that enters the second medium
changes its direction of propagation at the
boundary.
– This bending of the ray is called refraction.
Refraction, cont.
•The incident ray, the reflected ray, the refracted
ray, and the normal all lie on the same plane.
•The angle of refraction depends upon the
material and the angle of incidence.
sin θ2 v 2

sin θ1 v1
– v1 is the speed of the light in the first medium and
– v2 is its speed in the second.
Refraction of Light…
•The path of the light
through the refracting
surface is reversible.
– For example, a ray
travels from A to B.
– If the ray originated at B,
it would follow the line
BA to reach point A.
Following the Reflected and Refracted Rays
•Ray  is the incident ray.
•Ray  is the reflected ray.
•Ray  is refracted into the
lucite.
•Ray  is internally reflected
in the lucite.
•Ray  is refracted as it
enters the air from the lucite.
Refraction Details
•Light may refract into
a material where its
speed is lower.
•The angle of
refraction is less than
the angle of incidence.
– The ray bends
toward the normal.
Refraction Details…
•Light may refract into
a material where its
speed is higher.
•The angle of
refraction is greater
than the angle of
incidence.
– The ray bends away
from the normal.
Light in a Medium
•The light enters from the
left.
•The light may encounter an
electron.
•The electron may absorb
the light, oscillate, and
reradiate the light.
•The absorption and
radiation cause the average
speed of the light moving
through the material to
decrease.
The Index of Refraction
•The speed of light in any material is less than its
speed in vacuum.
•The index of refraction, n, of a medium can be
defined as
speed of light in a vacuum c
n

speed of light in a medium v
Index of Refraction…
•For a vacuum, n = 1
– We assume n = 1 for air also
•For other media, n > 1
•n is a dimensionless number greater than unity.
– n is not necessarily an integer.
Some Indices of Refraction
Frequency Between Media
•As light travels from one
medium to another, its
frequency does not change.
– Both the wave speed and
the wavelength do change.
– The wavefronts do not pile
up, nor are they created or
destroyed at the boundary,
so ƒ must stay the same.
Index of Refraction
•The frequency stays the same as the wave travels from one
medium to the other.
v = ƒλ
– ƒ1 = ƒ2 but v1  v2 so λ1  λ2
•The ratio of the indices of refraction of the two media can be
expressed as various ratios.
c
λ1 v1
n1 n2
 

c
λ2 v 2
n1
n2
•The index of refraction is inversely proportional to the wave
speed.
– As the wave speed decreases, the index of refraction increases.
– The higher the index of refraction, the more it slows downs the light
wave speed.
More About Index of Refraction
•The previous relationship can be simplified to
compare wavelengths and indices: λ1n1 = λ2n2
•In air, n1 = 1 and the index of refraction of the
material can be defined in terms of the
wavelengths.
λ
n
λn
 λ in vacuum 


λ
in
a
medium


Snell’s Law of Refraction
n1 sin θ1 = n2 sin θ2
– θ1 is the angle of incidence
– θ2 is the angle of refraction
•The experimental discovery of this relationship
is usually credited to Willebrord Snell and is
therefore known as Snell’s law of refraction.
Prism
•A ray of single-wavelength
light incident on the prism will
emerge at angle d from its
original direction of travel.
– d is called the angle of
deviation.
– F is the apex angle.
Huygens’s Principle
•Huygens assumed that light is a form of wave motion rather
than a stream of particles.
•Huygens’s Principle is a geometric construction for
determining the position of a new wave at some point based
on the knowledge of the wave front that preceded it.
•All points on a given wave front are taken as point sources for
the production of spherical secondary waves, called wavelets,
which propagate outward through a medium with speeds
characteristic of waves in that medium.
•After some time has passed, the new position of the wave
front is the surface tangent to the wavelets.
Huygens’s Construction for a Plane Wave
•At t = 0, the wave front is
indicated by the plane AA.’
•The points are representative
sources for the wavelets.
•After the wavelets have
moved a distance cΔt, a new
plane BB’ can be drawn
tangent to the wavefronts.
Huygens’s Construction for a Spherical Wave
•The inner arc represents
part of the spherical wave.
•The points are
representative points where
wavelets are propagated.
•The new wavefront is
tangent at each point to the
wavelet.
Huygens’s Principle and the Law of Reflection
•The law of reflection can be
derived from Huygens’s
principle.
•AB is a plane wave front of
incident light.
– The wave at A sends out a
wavelet centered on A
toward D.
– The wave at B sends out a
wavelet centered on B
toward C.
•AD = BC = c Δt
Huygens’s Principle and the Law of Reflection…
•Triangle ABC is congruent to triangle ADC.
•cos g = BC / AC
•cos g’ = AD / AC
•Therefore, cos g = cos g’ and g g’
•This gives θ1 = θ1’
•This is the law of reflection.
Huygens’s Principle and the Law of Refraction
•Ray 1 strikes the surface
and at a time interval Δt
later, ray 2 strikes the
surface.
•During this time interval,
the wave at A sends out a
wavelet, centered at A,
toward D.
Huygens’s Principle and the Law of Refraction…
•The wave at B sends out a wavelet, centered at B,
toward C.
•The two wavelets travel in different media, therefore
their radii are different.
•From triangles ABC and ADC, we find
sin θ1 v1

sin θ2 v 2
BC v1t
sin θ1 

AC AC
AD v 2t
and sin θ2 

AC AC
sin θ1 c n1 n2
But


sin θ2 c n2 n1
and so n1 sin θ1  n2 sin θ2
This is Snell’s law of refraction.
Dispersion
•For a given material, the index of refraction varies with
the wavelength of the light passing through the
material.
•This dependence of n on λ is called dispersion.
•Snell’s law indicates light of different wavelengths is
bent at different angles when incident on a refracting
material.
Variation of Index of Refraction with Wavelength
•The index of refraction
for a material generally
decreases with increasing
wavelength.
•Violet light bends more
than red light when
passing into a refracting
material.
Refraction in a Prism
•Since all the colors have
different angles of
deviation, white light will
spread out into a spectrum.
– Violet deviates the most.
– Red deviates the least.
– The remaining colors are
in between.
The Rainbow
•A ray of light strikes a drop of water in the
atmosphere.
•It undergoes both reflection and refraction.
– First refraction at the front of the drop
• Violet light will deviate the most.
• Red light will deviate the least.
The Rainbow...
•At the back surface the
light is reflected.
•It is refracted again as it
returns to the front surface
and moves into the air.
•The rays leave the drop at
various angles.
– The angle between the
white light and the most
intense violet ray is 40°.
– The angle between the
white light and the most
intense red ray is 42°.
Observing the Rainbow
•If a raindrop high in the
sky is observed, the red
ray is seen.
•A drop lower in the sky
would direct violet light to
the observer.
•The other colors of the
spectra lie in between the
red and the violet.
Double Rainbow
•The secondary rainbow is
fainter than the primary.
•The colors are reversed.
•The secondary rainbow
arises from light that makes
two reflections from the
interior surface before
exiting the raindrop.
•Higher-order rainbows are
possible, but their intensity
is low.
Total Internal Reflection
•A phenomenon called total internal reflection
can occur when light is directed from a medium
having a given index of refraction toward one
having a lower index of refraction.
Possible Beam Directions
•Possible directions of the
beam are indicated by rays
numbered 1 through 5.
•The refracted rays are
bent away from the
normal since n1 > n2.
Critical Angle
•There is a particular angle
of incidence that will
result in an angle of
refraction of 90°.
– This angle of incidence is
called the critical angle, θC.
sin θC 
n2
(for n1  n2 )
n1
Critical Angle…
•For angles of incidence greater than the critical
angle, the beam is entirely reflected at the
boundary.
– This ray obeys the law of reflection at the
boundary.
•Total internal reflection occurs only when light
is directed from a medium of a given index of
refraction toward a medium of lower index of
refraction.
Fiber Optics
•An application of
internal reflection
•Plastic or glass rods are
used to “pipe” light
from one place to
another.
•Applications include:
– Medical examination
of internal organs
– Telecommunications
Construction of an Optical Fiber
•The transparent core is
surrounded by cladding.
– The cladding has a
lower n than the core.
– This allows the light in
the core to experience
total internal
reflection.
•The combination is
surrounded by the
jacket.
Fiber Optics…
•A flexible light pipe is
called an optical fiber.
•A bundle of parallel
fibers (shown) can be
used to construct an
optical transmission
line.
Fresnel's Reflections
Doppler Effect for Light
• The change in frequency due to relative motion is called
Doppler effect.
𝑓 = 𝑓𝑜 1 − 𝑢/𝑐
• In non-relativistic range 𝑢/𝑐 is very small, so there is no
significant difference in the change of frequency when source
is stationary and observer is moving or observer is stationary
and source is moving with speed 𝑢.
• The velocity of stars are determined by using the Doppler
effect. The motion of a star causes a shift in the wavelengths
received.
• The amount of the shift depends in this way:
Δ𝜆
𝜆𝑜
=
𝑢
𝑐
/
where c
is the speed of light and u (radial velocity) is the component of
the star's motion that is along the line of sight.
• The radial velocity, 𝑢 =
∆𝜆
. 𝑐.
𝜆𝑜
Relativistic Doppler Effect
• The Doppler effect predicted by the theory of
relativity is
𝑓 = 𝑓𝑜
1−𝑢/𝑐
1−𝑢2 Τ𝑐 2
= 𝑓𝑜
1−𝑢/𝑐
1+𝑢/𝑐
when source and observer are moving away with
relative speed 𝑢.
• If the source and observer are approaching to each
other replace 𝑢 with −𝑢.
Relativity……
Momentum and kinetic energy at high speeds…………….
Transverse Doppler Effect
Doppler shift of light for an object moving
transversally to the observer:
• for an object moving transversally to an
observer, a line may be drawn between that
object and the observer, and it can be shown
that this line will reduce if the object is
approaching a sight line forming the nearest
approach of the object.
• An approaching object will appear blueshifted at which the object is approaching
along the sight line.
• A receding object will appear red-shifted
when the object is receding from the observer
along its sight line.