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1COMPOSSED AND WRITTEN BY PROF. NAJEEB MUGHAL. GOVT. MUSLIM SCIENCE DEGREE COLLEGE HYD.
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CHAPTER 9
NATURE OF LIGHT
Contents:
1. DUAL NATURE OF LIGHT.
2. INTEREFERNCE OF LIGHT.
3. YOUNG’S DOUBLE SLIT EXPERIMENT.
4. INTERFEROMETER.
5. THIN FLIM
6. DIFFRACTION
7. DIRRECTION GRATTING
8. X-RAYS DIFFRACTION
9. POLORIZATION OF LIGHT
10. SHORT DEFINITIONS.
11. EQUATIONS
12. SUMMARY
13. SHORT QUESTIONS AND ANSWERS.
TECHNECHAL TERM RELATIVE DEFINITIONS
1: Dual nature of light:
Light is an external cause responsible for sensation of vision Light is a form of energy. Energy can be transferred from
one point to another point either by particle motion or by wave motion. Accordingly, different theories on the nature of light have
been proposed. The important theories are as follows:
Aristotle was one of the first to publicly hypothesize as to the nature of light, proposing that it was a disturbance in the element
air. At the beginning of the 11th century, the Arabic scientist Alhazen wrote the first comprehensive treatise on optics; describing
refraction, reflection, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He
asserted that these rays were composed of particles of light.
Newton's Corpuscular Theory:
According to Sir Issac Newton's Corpuscular Theory, a luminous body continuously emits tiny, light and elastic particles
called corpuscles in all directions. When these particles fall on the retina of the eye they produce the sensation of vision.
This theory could explain a number of phenomena concerning light like rectilinear propagation reflection and refraction.
Reflection was explained by assuming that the corpuscles which fall on a smooth surface would bounce back like rubber balls
hitting a wall. When this theory was used to explain refraction scientists found that the velocity of light in a denser medium would
be more than that in a rarer medium. However, the experimental findings of Foucault pushed back the corpuscular theory of
Newton. This corpuscular theory could not explain satisfactorily certain other phenomena
Huygens' Wave Theory:
In 1967 Christian Huygens proposed the wave theory of light. According to this, a luminous body is a source of
disturbance in hypothetical medium called ether. The disturbance from the source is propagated in the form of waves through
space and the energy is distributed equally in all directions Even though this theory could satisfactorily explain several optical
phenomena, the presence of ether could not be detected
Young's Double-Slit Experiment:
In 1803, Thomas Young studied the interference of light waves by shining light through a screen with two slits equally
separated, the light emerging from the two slits, spread out according to Huygen's principle. Eventually the two wave fronts will
overlap with each other, if a screen was placed at the point of the overlapping waves, you would see the production of light and
dark areas (see interference). Later in 1815, Augustin Fresnel supported Young's experiments with mathematical calculations.
Maxwell's Electromagnetic Theory:
Electromagnetic theory of light was put forward by James Clerk Maxwell in 1873. According to this theory, light consists of
fluctuating electric and magnetic fields propagating in the form of electromagnetic waves. But this theory failed to explain the
photoelectric effect.
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Planck's Quantum Theory:
In 1900 According to Max Planck's Quantum theory, radiation is not continuous but is made up of tiny
packets of energy called photons. However, this theory could not explain other optical phenomena From all
the above theories it is clear that certain optical phenomena can be explained clearly only if light is
considered to be made up of particles, while certain other phenomena can be explained only if we consider
light as a wave.
In 1905 Albert Einstein had proposed a solution to the problem of observations made on the behavior
of light having characteristics of both wave and particle theory. From work of Plank on emission of light from
hot bodies, Einstein suggested that light is composed of tiny particles called photons, and each photon has energy.
Light Wave Theory:
Light can exhibit both a wave theory and a particle theory at the same time. Much of the time, light behaves like a wave.
Light waves are also called electromagnetic waves because they are made up of both electric (E) and magnetic (H) fields.
Electromagnetic fields oscillate perpendicular to the direction of wave travel, and perpendicular to each other. Light waves are
known as transverse waves as they oscillate in the direction traverse to the direction of wave travel.
De Broglie's wavelength:
In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter,[6][7] not just light, has a wave-like
h
nature; he related wavelength, and momentum . λ =
p
The Speed of Light:
The speed of light in a vacuum is a universal constant, about 300,000 km/s or 186,000 miles per second. The exact speed of
light is: 299,792.458 km/s It takes approximately 8.3 min for light from the sun the reach the earth.
Taking the distance of the sun from Earth into account, which is 150,000,000 km, and the fact that light travels at 300,000 km/s,
With the use of the SI units for wavelength (l), frequency (¦) and speed of light (c), we can derive some simple equations relating
c
to wavelength, frequency and speed of light: λ =
f
Photon Model of Light:
As proposed by Einstein, light is composed of photons, very small packets of energy. The reason that photons are able to travel
at light speeds is due to the fact that they have no mass and therefore, Einstein's infamous equation - E=mc2 cannot be used.
Another formula devised by Planck, is used to describe the relation between photon energy and frequency - Planck's constant (h)
= 6.63x10-34 Joule-Second. E = h f
hc
Thus, E =
, here, E is the photonic energy in Joules, h is Planks constant and f is the frequency in Hz
λ
Sources:
Light is produced by one of two methods 1. Incandescence is the emission of light from "hot" matter (T ≳ 800 K).
2. Luminescence is the emission of light when excited electrons fall to lower energy levels (in matter that may or may not be "hot").
Huygen’s principle and Wave front:
According to the “Huygen’s principle”,
“Every point on a wave front can be considered as a source of tiny wavelets that spread out in the forward direction at
the speed of the wave itself. The new wave front is the envelope of all the wavelets (that is the tangent to all of
them).The tangent will give a secondary spherical wave front”.
The energy flow equally in all directions of waves propagated. The direction of the energy,
in which the waves travel, is called a “ray”.
A “plane wave front” is a small portion of the spherical wave front, which is far away from the source.
Light year:
The distance traveled by light in one year is called light year. Thus light-year is a unit of distance.
One light year = velocity  time (in seconds in one year)
One light year = 3 108 m /sec (365.25  24  3600 sec) or light year = 9.461  1015 meter = 9.461 1012 km
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2.  Interference of light: 
The modification in the distribution of light energy due to superposition of two light waves is called
“Interference of light”.
There are two types interference. 1. Constructive interference and 2) Destructive interference.
Constructive interference:
Constructive interference occurs when the crests and the troughs of the two wave
trains coincide (the wave fronts are in phase. The resultant is the sum of the two
amplitudes.
Destructive interference:
Destructive interference occurs when the crests of one wave coincide with the troughs of
the other the wave fronts are not in phase. The resultant is the difference between the two
amplitudes
Conditions of interference of light:
1. the sources should be monochromatic (a light of single wave length.)
2. The sources should be coherent (the two sources having same phase difference. They
emit light waves of same frequencies and amplitude, with same wavelength.)
3. The sources should be narrow (the source should be as pinhole.)
The sources should be closer (the sources are placed near to one another.)
DESCRIPTIVE
PART
3. Young’s Double Slit Experiment: 
Introduction:
A British physicist in 1801 named Thomas Young was proved the wave nature of light by double slit experiment. In this
experiment, a single source is split in two, to generate two coherent sources. When
the light from the two sources is projected on a screen, an interference pattern is
observed.
Experiment:
Light from a point monochromatic source travel, towards two coherent sources
S1 and S2, after passing interfere each other finally the waves are made to fall on to
screen and visible pattern is obtained on to screen. At the center of the screen the
waves from the two sources are in phase. As we move away from the center, the
path traveled by the light from one source is larger than that traveled by the light from the other source. When the difference in
path is equal to half a wavelength, destructive interference occurs. Instead, when the difference in path length is equal to a
wavelength, constructive interference occurs. The screen consists a series of light having, dark and bright bands; they are
parallel to one another .The bands are known as “fringes”.
Description:
Two light of wavelength “”, pass through two slits, separated by a distance “d” and strike a screen a distance, “L”, from the
slits. You can change these parameters and see the interference on the screen on which bands are observed, the fringe
spacing is “y”. The path difference between two light waves is d sin, that light wave covered more from S2 as compared light
from S1.
Mathematical derivation:
For constructive interference, d sin  = m  - - - - - - ►eq.(1)
Where, m = 1,2, - - -n, is called order of the interference fringe.
Thus bright bands are observed, also called ‘maxima”.
1
for destructive interference d sin θ = ( m + ) - - - - - - - ►(2).
2
Where m= 1,2,- - - - n
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Then dark bands are observed, also called “minima”.
Consider OPC right-angled triangle
OP
Sin  = tan  =
, Because CP = CO ( base = hyp.)
CP
Y
Sinθ =
, The equation # 1, for brightness can be written as,
L
Y
d   =mλ
L
L
Yb = m λ  
d
And equation # 2, for darkness will be,
1
Y
d   = (m+ )λ
2
L
1 L

Yd =  m +  λ
2 d

The distance between two adjacent bright or dark fringes is called “fringe spacing”.
If, m = n and , m = ( n+1),
L
Then, Yb = n λ   , for m = n
d
L
And Yb =  n + 1 λ   , for m = (n+1)
d
Fringe spacing = Yb ( at n+1th fringe) - Yb ( at n th fringe)
L
L
 x = Yb =  n + 1 λ   – Yb = n λ  
d
d
Lλ
 Lλ
Lλ
Δx=n 
- n
+

d
 d 
 d 
Lλ
Δx=
d
Lλ
Hence,
Fringe spacing = Δ x =
d
4 :  Michelson interferometer: 
Introduction:
The American scientist Albert A. Michelson invented this interferometer. He
designed this instrument for the measurement of interference fringes. There are two paths from the
light source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and
then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes
through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent
mirror, then reflects from the semi-transparent mirror into the detector
Construction:
An interferometer constructed using a half-silvered mirror inclined at a 45° angle to the
incoming beam. Half the light is reflected perpendicularly and bounces
off a beam splitter; half passes through and is reflected from a second beam splitter.
The light passing through the mirror must also pass through an inclined
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compensator plate to compensate for the fact that the other ray
passes through the mirror glass three times instead of one.
Working:
A monochromatic light from a single point source is striking a half–
silvered mirror placed at 45o with incident beam. Light splits in to two equal intensity rays, after reflection
and refraction. After breaking half
of the beam, say ray-1 falls on to fixed mirror M1 , where it is reflected back. The
other half is refracted, say ray-2 falls on to movable mirror M2. Both mirrors are perpendicular to one
another, the rays cover equal distances after reflection and recombine on to silvered glass plate. At this stage the path
difference is zero between two rays. They interfere constructively, the bright fringe appears. The movable mirror M 2 is moved a
distance  /4, one beam will travel an extra distance say, path difference changes  /2. The two beams will destructively
interfere and dark fringe appears. Again the movable mirror is moved  /2, the path difference becomes , so that bright fringe
appears. This shows that alternatively bright and dark fringe appear. The reflected rays after striking with plane mirrors; they
recombine and produce interference pattern, which can be seen. The wavelength of light is the
measured
by counting the number of fringes “m”.
Suppose a movable mirror is moved “x’ distance and ‘m” bright or
dark fringes are appears.
Therefore,
2x=m
1 x
λ=
2  m 
Applications;
Interferometers can be used for many different purposes. Some examples are:
1
:for the measurement of a distance with an accuracy of better than an optical wavelength
2 :for
measuring the wavelength e.g. of a laser beam.
3: for
monitoring slight changes in an optical wavelength or frequency
4: for measuring rotations
5: or measuring slight deviations of an optical surface from perfect flatness
6: for measuring the line width of a laser
7: for revealing tiny refractive index variations or induced index changes
in a transparent medium
8: for measurements of the chromatic dispersion of optical components
9: as an optical filter
10: for the full characterization of ultra short pulses
6. Interference of light by Thin Films: 
In everyday life, the interference of light most commonly gives rise to easily
observable effects when light impinges on a thin film of some transparent material. For
instance, the brilliant colors seen in soap bubbles, in oil films floating on puddles of
water. A very thin film of air is trapped between two pieces of glass, as shown If
monochromatic light is incident normally to the film then some of the light is reflected
from the interface between the bottom of the upper plate and the air, and some is
reflected from the interface between the air and the top of the lower plate. The eye
focuses these two parallel light beams. The two beams produce either destructive or constructive interference, depending on
whether their path difference.
Let “t” be the thickness of the air film. The difference in path-lengths between the two light rays shown in the figure is. x = 2 t
Naively, we might expect that constructive interference, and, hence, brightness, would occur if 2 t = m λ , where “m” is an
1

integer, and destructive interference, and, hence, darkness, would occur if 2 t =  m +  λ . An additional phase difference is
2

introduced between the two rays on reflection. The first ray is reflected at an interface between an optically dense medium (glass),
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through which the ray travels, and a less dense medium (air). There is no phase change on reflection from
such an interface, just as there is no phase change when a wave on a string is reflected from a free end of
the string. The second ray is reflected at an interface between an optically less dense medium (air), through
which the ray travels, and a dense medium (glass). There is an 180 o phase change on reflection from such
an interface, just as there is an 180o phase change when a wave on a string is reflected from a fixed end.
Thus, an additional 180o phase change is introduced between the two rays, which is equivalent to an
λ
additional path difference of . When this additional phase change is taken into account, the condition for
2
1

constructive interference becomes 2 t =  m +  λ where “m” is an integer. Similarly, the condition for destructive interference
2

becomes 2 t = m λ
If the thin
film consists of water, oil, or some other transparent material of refractive index “n” then the results are basically the same as
λ
those for an air film, except that the wavelength of the light in the film is reduced from  (the vacuum wavelength) to . It follows
n
1

that the modified criteria for constructive and destructive interference are 2 n t =  m +  λ
and 2 n t = m λ
2

7. Newton Ring: 
Arrangement:
The convex surface of a long focal length lens (large radius of curvature) is placed in contact with a plane glass plate. A
thin film of air is formed between the two surfaces of glass in contact. There is no phase change at the glass-air surface of the
convex lens (because the wave is going from a higher to a lower refractive index medium)
Explanation
Suppose light of wave length ' ' falls on the lens, the radius of curvature of the convex lens is R and the radius of ring is 'r'. After
refraction and reflection two rays 1 and 2 are obtained. These rays interfere each other producing alternate bright and dark rings.
At the point of contact the thickness of air film is zero and the path difference is also zero and as an 180 O path difference occurs,
so they cancel each other and a dark ring is obtained at the centre.  BD  BE  =  AB BC
From the figure AB=t, BC =2R-t and BD = r
 r  r  =  t  2 R - t 
r2 = 2 R t - t2 
Where “t” is very small as compared to r, therefore t2 is negligible.
r 2 = 2 R t - - - - - - - ► (1).
1
In thin films, path difference for constructive interference is: 2 n t = (m + ) λ
2
Where n= refractive index. For air n = 1
1
2 t = (m + ) λ - - - - - - - ► (2).
2
For first bright ring m = 0 for second bright ring m = 1 for third bright ring m = 2
Similarly for Nth bright ring m = (N-1) Putting the value of m in equation (2)
1 

2 t =  N-1 + )  λ
2 

1

2 t = N - λ
2

Putting the value of’t’ in equation (1)
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1 
1
N -  λ
2 
2
1 
1 
r2 = 2 R   N -  λ 
2 
2 
1

r2 = R  N -  λ
2

t=
1

RN -  λ
2

This is the expression for the radius of Nth bright ring where
rn = radius of Nth bright ring,N = Ring number, R = radius of curvature of lens and  = Wave length of light
rn =
8. Diffraction: 
Diffraction is caused by light rays bending around sharp edges.
Definition:
The bending of light waves behind obstacles in to the shadow region is known as “Diffraction”.
Since diffraction occurs for waves, but not for particles, it can serve as one means for
distinguishing the nature of light.
When sunlight entered a darkened room through a tiny hole in a screen, the spot on the
opposite wall was larger than would be expected from geometric rays .The border of the image is
not clear but was surrounded by colored fringes. This is due to diffraction.
Types of Diffraction:
There are two types of diffraction known as Fresnel Deification and Fraunhofer Diffraction.
Fresnel Diffraction:
Fresnel diffraction a process of diffraction that occurs when a wave passes through an aperture and
diffracts in the near field, causing any diffraction pattern observed to differ in size and shape, depending on the distance
between the aperture and the projection. It occurs due to the short distance in which the diffracted waves propagate,
Fraunhofer Diffraction:
Fraunhofer diffraction is a form of wave diffraction that occurs when field waves are passed through an aperture
or slit causing only the size of an observed aperture image to change due to the far-field location of observation and the
increasingly planar nature of outgoing diffracted waves passing through the aperture.
9. Diffraction Grating: 
A diffraction grating is an optical device that consists of many thousands of apertures:
Each of these openings diffracts the light beam, but because they are evenly spaced
and the same in width, the diffracted waves experience constructive interference. A
large number of equally spaced parallel slits, is called “Diffraction grating”
Construction:
Using a diamond tip to role very fine lines on glass can make gratings. The
untouched spaces between the lines serve as gratings. A diffraction grating
containing slits is called a “transmission grating”.
Explanation:
Let us consider the parallel rays, of light are incident on grating. The slits are n
arrow enough, so that diffraction by each of them spreads light over wide angles
on a distant screen behind the grating and interference can occur with light from all
the other slits. Light rays through each slit without deviation
( = 0o)
interfere constructively to produce a bright line at the center of screen. After
diffraction through the grating makes an angle  with the normal to the grating
.The parallel rays are brought to focus on to the screen at P by convex lens. The
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path difference between two rays is (l) =r q = m , they overlap each other at position point P.
Mathematical derivation:
Where
m=rq
m = ( a + b ) Sin 
Where, a = separation between two constructive slits, and b = slit width.
Therefore, (a+b) = d, known as “Grating element”.
d = length of grating / Total number of lines ruled
It means,
m  = d Sin 
There are “m” order numbers of images (or pattern).
Spectroscope is a device to measure wavelengths accurately using diffraction
grating (or a prism), to separate different wavelengths of light. A diffraction grating spreads out
light into its component wavelengths, the resulting pattern is called “spectrum”.
10. Diffraction of X- rays: 
Definition of X-rays:
X- Rays are such type of light have shorter wavelength and higher frequency provides greater resolution when we
examining an object microscopically. X- Rays are electromagnetic radiation.
Description:
A very effective and complicated technique of X- ray’s diffraction has proved, for examining the microscopic world of atoms
and molecules. In a crystal such as NaCl or any other, the atoms are arranged in an orderly in a regular manner and at regular
spacing. This atom spacing is of the order of a few Angstroms and therefore the diffraction of X–rays takes place when they fall
on a crystal. The atoms in crystal might serve as three-dimensional diffraction grating for X –rays. It was suggested that crystals
could be used as grating for X- Ray’s diffraction
Explanation:
If X-rays are allowed to pass through a crystal, they can be diffracted from the parallel planes of atoms in the crystal.
The X – rays are found only along certain angles. An X-ray beam is incident atom a crystal of thickness “d”. It is found that beam
1 is reflected from upper surface of atoms and beam 2 from lower surface of atoms. The two beams interfere constructively and
path difference is 2 d sin,
Then 2 d sin  = m 
It is Bragg’s Law
11. Polarization of light waves: 
”The process of removal of undesired component of light is called polarization of
light waves”.
Sometime we want to remove undesired components from the light wave to reduce its
intensity, for this purpose we use phenomena of polarization. Sun glasses are the common
example of polarization.
Plane of polarization:
”The plane containing electric vector and direction of motion of the wave is called plane of
polarization".
If a light wave is polarized in the direction of positive y-axis and the direction of
propagation of polarized wave is in the positive x-axis then the x-y plane is called plane of
polarization. Similarly if light wave is polarized in positive z-axis and propagate in x-axis
then x-z plane is plane of polarization.
Polarizer:
"If a polarizing sheet is used to polarize the light then it is called polarizer".
If a sheet is used to remove the undesired component of the light from a light wave, then this sheet is called polarizer.
Analyzers:
"If a Polaroid disc is used to test the polarized light then it is called analyzer".
The disc which is used to check whether the light is polarized or non-polarized, then this sheet or disc is called analyzer.
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Equations
1. for bright fringe: y B = m λ
for fringe spacing : y = λ
1 L

2. for dark fringe: y D =  m+  λ
2 d

L
d
3.
L
d
1

4. For bright Fringe : 2 n t =  m +  λ
2

5. For dark Fringe : 2 n t = m λ
1

6. For bright Fringe :Y=  N -  R λ
2

length of plate  L
8. Diffracting Element  d  =
Number of openings  N 
7. For dark Fringe :Y=
9. d sin θ =  m
NRλ
10 2d sin θ =  m bragg’s equation
Dimensions
PHYSICAL QUANTITY & SYMBOL DIMENSION
Fringe spacing y = λ
L
d
Diffracting element
d  =
y
length of plate  L 
Number of openings  N 
 L L
 L
d=
UNIT
  L
 L
No dimension
meter
  L
meter
Short questions
Q. # 1 whither a path difference of ( / 4) are associated with a constructive interference or destructive
interference or neither of them.
Answer:
When a path difference of ( / 4) are associated with a constructive interference or destructive interference then
no any interference takes place.
Q. # 2: What are the conditions between two waves that interfere (a) constructively (b) destructively?
Answer:
When path difference = 0, ,2, - - - - - - n , the interference will be constructive .
λ 3λ 5λ
1

,
,
- - - - - -  n +  λ , the interference will be destructive.
And when path difference =
2 2 2
2

Q. # 3:
What aspect of the nature of light is proved by the phenomenon of polarization?
Answer:
In a transverse wave, the vibration is perpendicular to the direction of propagation. If the vibration of all parallel,
the wave is said to be plane polarizes. The vibration and propagation lines determine a plane. This is called the
“plane of polarization”.
Q. # 4:
Describe the use of a pilloried as an analyzer and polarize.
Answer:
"If a Polaroid disc is used to test the polarized light then it is called analyzer".
"If a polarizing sheet is used to polarize the light then it is called polarizer".
Q. # 5:
What is difference between interference and diffraction of light?
Answer:
INTEREFENCE
DIFFRACTION
1. It is due to two waves of light coming from same
1. This pattern is produced by the interaction of source,
which may support or cancel each other
light coming out from different parts of same wave
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2. Interference fringes may or may not be of same width. 2. Diffraction fringes can never be of
same width.
3. The pattern points of minimum intensity are
3. Diffraction points of minimum
intensity are not perfectly dark.
Perfectly dark
4. All bright bands are of uniform intensify
4. All bright bands are not of uniform
intensity.
5. It is possible without diffraction.
5. It is interference of the deviated
waves
Q. # 6:
What are the main facts, which support the following statement?
(a) The light is wave motion and not corpuscular (b) the light travels in the form of transverse waves (c) Light
waves are much shorter than sound waves
Answer:
Q. # 7: What is the principle of interference of light?
Answer:
Two set of waves (such as light) can combine with each other to produce a resultant wave. The way in which this
combined wave is produced is called interference
Q. # 8: What are conditions necessary for interference of light?
Answer:
Following are the conditions of interference of light:
1. the sources should be monochromatic .
2. The sources should be coherent
3. The sources should be narrow .
4 .The sources should be closer.
Q. # 9:
Give an account of spectrum produced by diffraction grating. How does it differ from that of a
prism?
Answer:
Q. #10: Was light a mechanical or non-mechanical wave?
Answer:
all previously known waves were mechanical and needed a medium
Q. # 11: What was Newton's contribution to light theory?
Answer:
Sir Isaac Newton in 1704. Newton, who had discovered the visible spectrum in 1666, held that light is composed of
tiny particles, or corpuscles, emitted by luminous bodies. By combining this corpuscular theory with his laws of
mechanics, he was able to explain many optical phenomena.
Q. # 12: What was Christiaan Huygens' theory about light?
Answer:
He developed a wave theory of light opposed to the corpuscular theory of Newton and formulated Huygens's
principle, which holds that, concerning light waves, every point on a wave front is itself a source of new waves. In
1678 he discovered the polarization of light by double refraction in calcite.
Q. #13: What is the present idea about the nature of light?
Answer:
It is believed that light travels in waves and is made up of mass less particles called photons. These waves propagate
at a constant speed, 3x108 m/s. Nothing can travel faster than this speed and nothing can travel the speed of light if it
is not mass less
Q. # 14: Explain Difference between diffraction and interference?
Answer:
Diffraction is the bending of waves around an obstacle, while interference is the meeting of two waves. For
instance, diffraction is what results from a pinhole blocking a wave source; the wave spreads out from that one point.
This effect is what creates shadows, regions where the light source is blocked but it is not completely dark.
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Interference, however, results from two waves colliding with one another undergoing constructive
and destructive interference, as in two chords being played. I think the confusion concerning
these two different phenomena is the fact that two pinholes, two diffraction sources, results in
interference of two sources, which is what the diffraction grating is, which creates the
characteristic bands of light and dark interference patterns.
Q. #15: Phenomena such as diffraction and interference can most easily be explained in the
terms of the?
Answer:
Phenomena such as diffraction and interference can most easily be explained in the terms of the wave properties of light.
Q. # 16: How is interference involved in light waves?
Answer:
The relative positions of light and dark lines depend upon the wavelength of the light, among other factors. Thus, if
white light, which is made up of all colors, is used instead of monochromatic light, bands of color are formed
because each color, or wavelength, is reinforced at a different position.
Q. # 17: What is an interferometer?
Answer:
The thickness of a very thin film such as the soap-bubble wall can be measured by an instrument called the
interferometer.
Q. # 18: What is destructive interference?
Answer:
Two light waves occurring simultaneously and having the same intensity neutralize each other if the rarefactions of
the one coincide with the condensations of the other, i.e., if they are of opposite phase. This canceling is known as
destructive interference.
Q. # 19: How is energy conserved during interference of light?
Answer:
There are regions where intensity (or if you prefer, photon probability) decreases (destructive interference), regions
where it increases (constructive interference), and it can be shown that if you integrate over the whole of space, the
total is unchanged.
Q. # 20: What is Monochromatic Light?
Answer:
Monochromatic light is light made of one colour it is coming from the word mono which means one.
Q. # 21: How is interference observed?
Answer:
Interference is observed in both sound waves and electromagnetic waves, especially those of visible light and radio.
Q. # 22:What is wave front?
Answer:
A scientist Christian Huygens considered that “A light waves in a line on a surface in the path of an advancing
wave on which all particles are in same phase is called wavefront.” The wave line of a wave emitting from a source
and traveling away from the source. The characteristics of wave front are: 1. it is at right angle to the direction of
travel of wave. 2. A line normal to wave front, indicating the direction of motion of waves is called a ray.
Q. # 23: What is the wavelength range of visible light?
Answer:
The wavelengths of visible light range from about 350 or 400 nm to about 750 or 800 nm.
Q. # 24: What is “coherent” light?
Answer:
Light that is all of the same wavelength and phase (all the waves are in step with one another) is called "coherent."
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Q. #25: When light under goes refraction. What happens to its frequenc`y?
Answer:
The frequency of the light wave doesn't change during refraction, reflection, interference etc...
The frequency is constant and depends upon the source o the light.
Only the velocity and wavelength of the light changes during refraction.
If you hold a torch over a swimming pool and keep your head inside water and look at it, you will
see a different colour coming from the torch. This is because the wavelength of light changes. If
you measure frequency by any method you'll find it’s the same. They do take a real deep breath
before you enter the pool to do all this
Q. # 26: What is the meaning of diffraction of light?
Answer:
Light has property that it tends to bend round sharp edges and spread into regions where it is not supposed to be.
On the other hand if light were composed of particles a burst of particles would always follow a straight line
trajectory. Such property is called Diffraction of light.
Q. # 27: Explain Young's double slit experiment?
Answer:
If coherent light is passed through two slits of the right size and separation then light and dark bands are seen
on a screen at the correct distance fronts the slits. This demonstrates the wave nature of light. The light is amplified
where two crests arrive at the same time and no light arrives when a crest and a throw arrive at the same time. This
experiment can also be done with electrons, with similar results.
Q. # 28: Why Newton’s ring is circular?
Answer:
Newton’s ring is circular because of the constant thickness on the locus of the circle from a fixed point
Q. # 29: Which phenomenon causes polarization of light?
Answer:
Light is usually unpolarized, it becomes polarized when it passes through a polarizing filter. Light can be polarized
because it travels as a transverse wave orthogonally to the direction of the medium in all directions, and polarizing
filters polarize light in one plane. Polarized filters in the vertical plane only allow light in the vertical plane to pass
through. Ex. polarized sunglasses have a polarizing filter in the vertical plane in order to minimize glare which is
polarized light in the horizontal plane. And yes polarizing filters can be rotated to polarize light in other planes as
well.
Q. # 30: Does a mirror polarize the light?
Answer:
Polarized light waves are light waves in which the vibrations occur in a single plane. The process of transforming
unpolarized light into polarized light is known as polarization. There are a variety of methods of polarizing light.
Q. #31: Discus the statment that diffraction gratings could just as will be called an interference grating?
Answer:
When a large number of sources produce interference pattern, the phenomenon is called diffraction. It can
be viewed as interference arising from superposition of large number of waves. Thus to call a diffraction grating an
interference grating is equally same.
Q. # 32: What is the difference between deviation and diffraction?
Answer:
Deviation is the change in path when wave enter one medium from another. Diffraction is the change in path
due to the bending of wave round opaque obstruct and spreading of wave through all angles
Deviation produces spectrum due to refractive index change and is obtained only on one side of the central position.
Diffraction produces spectrum due to the interference after bending round corners and it is obtained on both sides of
central position.
Q. # 33: What is Huygen's Principle?
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Answer:
Huygens's Principle: States that “every point on a propagating wave front serves as the
source of spherical secondary wavelets, such that the wave front at some later time is the
envelope of these wavelets. If the propagating wave has a frequency, f, and is transmitted through
the medium at a speed, v, then the secondary wavelets will have the same frequency and speed”.
Q. # 34: In the young’s experiment, one of the slits is covered with blue filter and other with red
filter. What would be of light intensity on the screen?
Answer:
The blue and red lights are not being in phase coherence due to different wave lengths. Therefore, no interference
pattern observed on screen. We observe only two colored images on the screen.
Q. # 35: Explain whether the young’s experiment is an experiment for studying interference or diffraction effect
of light?
Answer:
The young’s double slit experiment is actually the overlapping of two light waves and produced interference
effect. Where diffraction is the bending of light around the sharp edges of slits. Interference experiment is also used
to study the diffraction phenomenon, as it occurs with the interference experiment. Thus the young’s experiment is
an experiment for studying interference of light.
Q. # 36: An oil film spreading bovver a wet foot path shows colors. Explain how does it happen?
Answer:
An oil film spreading bovver a wet foot path shows colors are due to interfernce of light waves .When a light
beam is incident then partially reflected from the upper surface of oil and partially reflected from the lower (inner)
surface of thin film. The two reflected beams are coherent and interfere each other. Thus constructive and
destructuive inteefernce takes place. Hence colors are observed.
Q. #37: How would you distinguish between unpolarized and plane polarized lights?
Answer:
The unpolarized and plane polarized light can be distinguished using a polarizer. If a polarizer is rotated in front
of incident unpolarized light a component of light will pass in each orientation. In case of plane polarized light, at
some particular orientation, no light will pass through at all.
Q. # 38: Can visible light produce interference fringes?
Answer:
Yes, visible light can produce interference fringes but each wavelength will produce its own interference fringes
and hence pattern will then be colored. The color at each point depends on witch wavelengths are reinforced by
interference.
Q. # 39:What is difference between Fresnel diffraction and Fraunhofer Diffraction?
Answer: Fresnel diffraction
1. The source of light and screen are kept at finite distance from the diffracting object. It is field diffraction
2. No lenses are used to make light rays parallel or convergent.
3. The incident wave front is not plane but is either spherical or cylindrical. The corresponding rays are not parallel.
4. The secondary wavelets do not possess same [phase at all points in the plane of obstacle.
5. The diffraction pattern arises due to the interference of secondary wavelets from various points on the unblocked
portion of wave front.
6. The center is always maximum intensity.
7. It produced when light suffers diffraction at straight edges, narrow slits, a thin wire, a small aperture, etc. .
Fraunhofer Diffraction
1. The source of light and screen are kept at an infinite distance from the diffracting object. So it is far-field
diffraction.
2. Two convex lenses are used; one of the lenses is used to make the light from the source parallel while the other
used to focus the light after diffraction on the screen.
3. The incident wave front is pane. The corresponding ray is parallel.
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4. The secondary wavelets are in phase at every point in plane of obstacle.
5.The diffraction pattern arises due to the interference between the waves fronts have been
deviated by diffracting objects.
6. The center may be a maximum or minimum intensity.
7. It produced when light suffers diffraction at a single slit, multiple slits, diffraction grating, etc.
Q. # 40: In youg’s double slit experiment following parameters have to dowith the light on
the screen? i) Distance between silts ii) width of slits iii) Wave length of incident light
Answer:
L
1
i) Since y = λ , this shows that y 
d
d
ii) The larger the width of slits, the intensity of pattern increases, but fringes become more blurred.
L
iii) Since y = λ , this shows that y  λ
d
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 The visible spectrum and dispersion:
The color of light is related to wavelength or frequency of light. Visible light- that to which our eyes are sensitive –fall in the
wavelength range of about 400nm to 750nm, this is known as the “visible spectrum”, and with in it lie different color s from violet
to red. Light with wavelength shorter than 750 nm is called infrared. Human eyes are not sensitive to ultraviolet or infrared, some
types of photographic film do respond to them. The index of refraction is greater for the shorter wavelength; violet light is bent
the most and the least as indicated. This spreading of white light into full spectrum is called “dispersion”.
Speed of light:
The speed of light in a vacuum is represented by the letter “c” from the Latin celeritas — swiftness. Measurements of the speed
of light.
 The speed of light in a vacuum is a universal constant in all reference frames.
 The speed of light in a vacuum is fixed at 299,792,458 m/s by the current definition of the meter.
 The speed of light in a medium is always slower the speed of light in a vacuum. The speed of light depends upon the
medium through which it travels. The speed of anything with mass is always less than the speed of light in a vacuum.
 Other characteristics
The amplitude of a light wave is related to its intensity.
1. Intensity is the absolute measure of a light wave's power density.
2. Brightness is the relative intensity as perceived by the average human eye
The frequency of a light wave is related to its color.
1. Color is such a complex topic that it has its own section in this book.
2. Monochromatic light is described by only one frequency.
3. Laser light is effectively monochromatic.
4. There are six simple, named colors in English each associated with a band of monochromatic light. In order of increasing
frequency they are red, orange, yellow, green, blue, and violet.
5. Light is sometimes also known as visible light to contrast it from "ultraviolet light" and "infrared light"
6.Other forms of electromagnetic radiation that are not visible to humans are sometimes also known informally as "light"
7. Polychromatic light is described by many different frequencies.
8. Nearly every light source is polychromatic.
9. White light is polychromatic.
A graph of relative intensity vs. frequency is called a spectrum (plural: spectra).
Although frequently associated with light, the term can be applied to any wave phenomena.
1. A continuous spectrum is one in which every frequency is present within some range.
2. Blackbody radiators emit a continuous spectrum.
3. A discrete spectrum is one in which only a well defined set of isolated frequencies are present. (A discrete spectrum is a finite
collection of monochromatic light waves.)
4. The excited electrons in a gas emit a discrete spectrum.
The wavelength of a light wave is inversely proportional to its frequency.
1. Light is often described by it's wavelength in a vacuum.
2. Light ranges in wavelength from 400 nm on the violet end to 700 nm on the red end of the visible spectrum. Phase differences
between light waves can produce visible interference effects.
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M M A
R
Y
 Light must travel through a medium. This medium is called Ether, which is an omnipresent, boundlessly
resilient, massless medium unable to be sensed that was formerly theorized as the medium that carried light. Light
is a form of energy - Light travels in waveform in short wavelengths. the concept of "ether" (the medium) was
invented, but the investigators Michelson and Morley`s made experiments demonstrating that ether does not exist.
Simultaneously, they also demonstrated a more important fact: The speed of light is constant. Light is a transverse,
electromagnetic wave that can be seen by humans.  Interference takes place when waves interact with each other,
while diffraction takes place when a wave passes through an aperture. These interactions are governed by the
principle of superposition. Interference, diffraction, and the principle of superposition are important concepts to
understanding several applications of waves. a diffraction grating, first developed in the 1870s by American
physicist Henry Augustus Rowland From diffraction patterns we can: • measure the average spacing between layers
or rows of atoms; • determine the orientation of a single crystal or grain; • find the crystal structure of an unknown
material; and • measure the size, shape and internal stress of small crystalline regions.
S H O R T D E F I N I T I O N
In dynamic equilibrium, a photon formed by two particles whose electric charges are opposed, and for this
reason they attract each other. This attraction is equilibrated by the centrifugal force generated when rotating
one with the other. By rotating electrical charged particles, a perpendicular magnetic field is generated, also
perpendicular to a stationary observer
Interferometry:
It is the technique of diagnosing the properties of two or more waves by studying the pattern of
interference created by their superposition. The instrument used to interfere the waves together is called an
interferometer.
Astronomical interferometer: It is an array of telescopes or mirror segments acting together to probe
structures with higher resolution. Astronomical interferometers are widely used for optical astronomy,
Michelson stellar interferometer: It is one of the earliest astronomical interferometers built and used. The
interferometer was proposed by Albert Michelson in 1890.
radio interferometer: An array of antennas operating as a single instrument of high angular resolution.
electromagnetic spectrum It is the range of all possible frequencies of electromagnetic radiation. The
"electromagnetic spectrum" of an object is the characteristic distribution of electromagnetic radiation emitted or
absorbed by that particular object.
Ultraviolet light:
The amount of penetration of UV relative to altitude in Earth's ozone Next in frequency comes
ultraviolet (UV). This is radiation whose wavelength is shorter than the violet end of the visible spectrum, and longer than that
of an x-ray.
X-rays:
UV come X-rays, which are also ionizing, but due to their higher energies they can also interact with matter.
Hard X-rays have shorter wavelengths than soft X-rays. As they can pass through most substances,
Gamma rays: After hard X-rays come gamma rays, which were discovered by Paul Villard in 1900. These are the
most energetic photons, having no defined lower limit to their wavelength.
Infrared radiation: The infrared part of the electromagnetic spectrum covers the range from roughly 300 GHz (1
mm) to 400 THz (750 nm). It can be divided into three parts:1. Far-infrared, from 300 GHz (1 mm) to 30 THz (10
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μm). The lower part of this range may also be called microwaves. 2.Mid-infrared, from 30 to
120 THz (10 to 2.5 μm). Hot objects (black-body radiators) can radiate strongly in this range. It is
absorbed by molecular vibrations, where the different atoms in a molecule vibrate around their
equilibrium positions.3. Near-infrared, from 120 to 400 THz (2,500 to 750 nm). Physical
processes that are relevant for this range are similar to those for visible light.
Scattering of Light: When light passes through a substance or gas, a part of it is absorbed and
the rest scattered away. The basic process in scattering is absorption of light by the molecules
followed by re-radiation in different directions. The strength of scattering can be measured by the
loss of energy in the light beam as it passes through the medium. In absorption the light energy is converted into the
internal energy of the medium and in scattering the light energy is radiated in other directions. The strength of
scattering depends on the size of the particle causing the scattering and the wavelength of light
Huygens' Principle: Every point of a wave front may be considered the source of secondary wavelets that spread
out in all directions with a speed equal to the speed of propagation of the waves.
diffraction grating :A diffraction grating is an optical device that consists of not one but many thousands of
apertures: Rowland's machine used a fine diamond point to rule glass gratings, with about 15,000 lines per in (2.2
cm). Diffraction gratings today can have as many as 100,000 apertures per inch. The apertures in a diffraction grating
are not mere holes, but extremely narrow parallel slits that transform a beam of light into a spectrum.
Diffractometer: A diffractometer can be used to make a diffraction pattern of any crystalline solid. With a
diffraction pattern an investigator can identify an unknown mineral, or characterize the atomic-scale structure of an
already identified mineral.
Crystalline material: A crystal is constructed of atoms or molecules arranged in a regular pattern in space. It is
this regularity which is responsible for diffracted beams. If the arrangement of atoms was random then the scattered
beams would randomly add together and also randomly cancel each other. They would not reinforce each other in
any direction to give diffracted beams.
electron diffraction: Most electron diffraction is performed with high energy electrons whose wavelengths are
orders of magnitude smaller than the interplanar spacings in most crystals. For example, for 100 keV electrons  <
3.7 x 10-12 m. Typical lattice parameters for crystals are around 0.3 nm.Electrons are charged, light particles and their
penetration into solids is very limited.
prism : A prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles
between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a
triangular base and rectangular sides, and in colloquial use "prism" usually refers to this type
dichroic prism :A dichroic prism is a prism that splits light into two beams of differing wavelength (colour). They
are usually constructed of one or more glass prisms with dichroic optical coatings that selectively reflect or transmit
light depending on the light's wavelength.
Total internal reflection : It is an optical phenomenon that occurs when a ray of light strikes a medium
boundary at an angle larger than a particular critical angle with respect to the normal to the surface. If the refractive
index is lower on the other side of the boundary, no light can pass through and all of the light is reflected. The critical
angle is the angle of incidence above which the total internal reflection occurs.
refractive index :The refractive index of a medium is a measure of how much the speed of light (or other waves
such as sound waves) is reduced inside the medium. The refractive index, n, of a medium is defined as the ratio of
the velocity, c, of a wave phenomenon such as light or sound in a reference medium to the phase velocity, vp.
Reflection: It is the change in direction of a wave at an interface between two different media so that the wave
returns into the medium from which it originated.
diffuse reflection.: When light strikes a rough or granular surface, it bounces off in all directions due to the
microscopic irregularities of the interface. Thus, an 'image' is not formed. This is called diffuse reflection.
Neutron reflection: Materials that reflect neutrons, for example beryllium, are used in nuclear reactors and
nuclear weapons. In the physical and biological sciences, the reflection of neutrons off atoms within a material is
commonly used to determine its internal structure.
Seismic reflection: Seismic waves produced by earthquakes or other sources (such as explosions) may be reflected
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by layers within the Earth. Study of the deep reflections of waves generated by earthquakes has
allowed seismologists to determine the layered structure of the Earth. Shallower reflections are
used in reflection seismology to study the Earth's crust generally, and in particular to prospect for
petroleum and natural gas deposits.
Refraction: It is the change in direction of a wave due to a change in its speed. This is most
commonly observed when a wave passes from one medium to another. Refraction of light is the
most commonly observed phenomenon, but any type of wave can refract when it interacts with a
medium,
Nicol prism : A Nicol prism is a type of polarizer, an optical device used to generate a beam of polarized light. It
was the first type of polarizing prism to be invented, in 1828 by William Nicol.
Particles
 have mass (inertia)
 respond to forces (acceleration)
 have momentum (mass x velocity)
Waves
 transfer energy from one place to another
 mechanical (require a medium) and non-mechanical
Particle Nature of Light Particle Nature of Light
Newton's Corpuscular Theory of Light (1670)
 light corpuscles have mass and travel at extremely high speeds in straight lines
 rectilinear propagation - blocked by large objects (well-defined shadows)
 obey the law of reflection when bounced off a surface
 speed up when they enter denser media (gravitational force of attraction, net F = ma)
 paths in denser media "bend towards the normal"
 prism dispersion - contradicted corpuscular theory
Wave Nature of Light
Huygens Principle (1680)
 wavelet envelop model (each point on a wavefront acts as a source for the next wavefront)
 plane waves generate plane waves, circular waves generate circular waves
 light was composed of longitudinal waves like sound
 obey the law of reflection when bounced off a surface
 waves slowed down when they entered a denser medium causing their paths to "bend towards the normal"
 light SHOULD produce interference patterns and diffraction patterns
Thomas Young's Double Slit Experiment (1807)
 bright (constructive) and dark (destructive) fringes seen on screen
 wave nature of light
 Diffraction vs Interference Patterns
diffraction fringes seen within and around a small obstacle or through a narrow opening
 wave nature of light
Young and Fresnel argue that light was a transverse wave (1820)
 polarization (iceland spar; polaroid filters)
 wave nature of light
Atomic Models
Beginning of the 20th century:
 atoms were electrically neutral - equal amounts of + and - charge
 the negative charge is associated with cathode rays (electrons) particles having very small mass
 atoms are stable
J. J. Thomson (1900)
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 discovered the electron - cathode rays
 plum-pudding model - electrons and protons evenly spread throughout the atom (diameter =
10-10 meters)
Max Planck (1900)
 blackbody radiation
 ultraviolet catastrophe
 E = hf where f = c/λ
Brownian Motion (1827)
 discovered initially by Scottish botanist, Robert Brown, when he witnessed pollen grains "jiggling" when
examined under a microscope - later he saw the same agitated behavior with dust particles and grains of soot
 "Brownian Motion" is now known to be the result of the collisions between neighboring atoms/molecules
(Einstein - 1905)
Rutherford's gold foil experiment (1909) with Geiger and Marsden (repeated with carbon and aluminum)
 1 out of every 8000 alpha particles scattered through an angle > 90°
 discovered a small positively charged nucleus (diameter ≤ 10-14 meters)
 the value of the charge needed from the scattering data would equate to the magnitude of the charge held in the
nucleus - which would dictate the number of electrons surrounding the nucleus which closely matched the atomic
number in Mendeleev's periodic table (1869)
Bohr model (1913) how were these electrons arranged?
 steady orbitals - deBroglie wavelengths
 energy levels - light emission, light absorption - excitation and de-excitation
 spectral lines
Franck/Hertz (1914) experimentally verified discrete energy levels
 bombarded room temperature mercury vapor with electrons of specific KE
 absorption peak at 4.9 eV which was then shown to represent the energy of the 254 nm wavelength in mercury's
emission spectrum
James Chadwich (1932)
 discovered the neutron
Werner Heisenburg (1935)
 first proposed the neutron-proton theory of nuclear structure
Parti Photoelectric effect (1905)
 light is made of photons
 quantized packets of radiant energy
 one photon emits one photo-electron
 current is proportional to the intensity of the light
 KE of the emitted photo-electrons is proportional to the frequency of the light
Compton Effect (1923) - bombarded graphite crystals with x-rays
 electrons were released - the momentum of the electrons revealed their KE which matched the energy lost by the
x-rays - a classic collision had occured in which momentum was conserved
 x-rays have momentum
from special relativity E = mc2
momentum (p) = mv = (E/c2)(v)
for light, v = c
therefore p = E/c
since E = hf = h(c/λ),
p = (hc/λ)/c
p = h/λ
 photons (quantized bundles of radiant energy) which have no mass do have momentum
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Wave Nature of Particles
deBroglie wavelength (1923)
 λdeBroglie = h/mv
 an integer multiple of an electron's deBroglie wavelength produced a steady state orbital
Davisson-Germer Experiment (1927)
 diffraction of electrons through a crystal revealed the same pattern as x-rays diffracted
through the crystal
 high energy electrons have wavelengths
 electron microscopes
Dual Nature of Matter
Schrodinger's Wave Mechanics (1926)
 quantum mechanical (mathematical) model
 clouds of electrons - probabilities
Max Born (1933)
 electron diffraction - interference pattern of electrons through double slits
 statistical interpretation of many electrons not the exact behavior of each individual electron
non-collapsing matter
 deBroglie wavelengths
 fermions must obey the Pauli Exclusion Principle (1925)
Heisenburg's Uncertainty Principle (1927)
 photons interact with one electron not all of them
 interference of localized wave disturbances creates a wave packet which has appreciable amplitude in only a
small region of space - acting like the motion of a particle
Δx Δp ≥ h/(2π)
ΔE Δt ≥ h/(2π)
Standard Model (1960's)
Fundamental Particles
 up, charm, top (+2/3)
 down, strange, bottom (-1/3)
 electron, muon, tau (-1)
 electron neutrino, muon neutrino, tau neutrino
proton composition (uud) yields a charge of +1
neutron composition (ddu) yields a charge of 0
Bosons vs Fermions
 gauge bosons (force carriers) can march in step (photons, W and Z bosons, gluons)
 fermions (leptons: electron, muon, tau; and quarks) must obey the Pauli Exclusion Principle (1925)
Four Fundamental Forces
 weak nuclear (W-, W+ and Zo producing natural radioactivity)
 strong nuclear (gluons and quarks confinement)
 electromagnetic (photons)
 gravitation (gravitons)
What causes mass?
 Higgs boson (postulated in 1960 but still not experimentally verified)
Yougs Double Slit Experiment Observations
If light is a particle…We set up our screen and shine a bunch of monochromatic light onto it.
If light is a particle, then only the couple of rays of light that hit exactly where the slits are will be able to pass
through. Imagine it as being almost as though we are spraying paint from a spray can through the openings. Since
they are little particles they will make a pattern of two exact lines on the viewing screen
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If light is a wave…If light is a wave, everything starts the same way, but results we get are very
different. There are still only two light rays that actually go through the slits, but as soon as they
pass through they start to diffract. Remember, diffraction is when light passes through a small
opening and starts to spread out. This will happen from both openings
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