Download Waves All Around Us!

PHYSICS
COURSE CODE: PH101
COURSE MATERIALS
1. PHYSICAL OPTICS
2. RELATIVITY
3. RADIATION
4. ATOMIC STRUCTURE
5. STATISTICAL DISTRIBUTIONS
6. LASERS
TEACHING PROCESS
The whole course will be covered through
1. Lectures
2. Tutorials
3. Laboratory
The topics will be covered in the lectures.
Assignments in the form of Questions will be
given.
Students have to complete the assignments
through discussion in tutorials.
Class tests will be conducted during tutorials.
Evaluation scheme
There will be three tests all over the semester.
20 marks for the Test-I.
25 marks for the Test-II.
30 marks for the TEST-III.
25 marks for internal assessment and class tests.
100 marks for the laboratory work.
Evaluation will be done through regular assessment of
practical and viva-voca.
PHYSICAL OPTICS
BOOKS:
• OPTICS, Eugene Hecht, Pearson Education.
• OPTICS, Ajay Ghatak.
• Fundamental of Optics, Jenkins & White.
• A. Beiser, Concepts of Modern Physics,
Optical Recording
• Media types:
– Compact Disc (CD)
– Digital Video/Versatile Disc (DVD)
• Reading technique:
– Reflect laser light from optical surface
– Measure reflected intensity to obtain
information
Techniques
• Laser light is focused
on disc aluminum layer
• Reflection is weaker
from ridge than flat
• Reflected light is
directed to photodiodes
• Light intensity
indicates ridges or flats
Most of the above applications need some
optical phenomena
Interference, Diffraction, Polarization
Physical Optics
OPTICS
Physical Optics
Wave nature of light
Interference
Diffraction
Polarization
Waves All Around Us!
Waves are everywhere. Sound waves, visible
light waves, radio waves, microwaves, water
waves, sine waves, cosine waves, telephone
chord waves etc.
There are a variety of phenomenon in our
physical world which resemble waves so
closely that we can describe such
phenomenon as being wavelike.
Wave
A wave is a disturbance that propagates,
carrying energy, which can travel
through either in a medium or through
vacuum, waves can transfer energy
from one place to another without any
displacement of the particles of the
medium.
Waves are characterized by crest
(highs) and trough(lows)
THERE ARE TWO TYPES OF COMMON
WAVES.
I) SOUND WAVE
II) LIGHT WAVE
Physical description of a wave
waves of various frequencies; the lower waves have higher
frequencies than those above.
Frequency is the measurement of the number of times
that event occurs repeatedly per unit time. To calculate
the frequency, one fixes a time interval, counts the
number of occurrences of the event within that
interval, and then divides this count by the length of
the time interval.
Amplitude is a nonnegative scalar measure of a
wave's magnitude of oscillation. The y is the
amplitude of the wave.
The wavelength is the distance between repeating
units of a wave pattern
Phase
The phase of a wave relates the position of a feature,
typically a peak or a trough of the waveform, to that
same feature in another part of the waveform.
positions of the peaks (X), troughs (Y) and zero-crossing points (Z)
coincide. The phase difference of the waves is thus zero
The phase difference between two signals of the same
frequency can be thought of as a delay or advance in the
start of one signal's cycle with respect to another.
Phase difference is expressed in degrees from 0 to 360. If the
difference is 180 degrees then the two signals are said to be in
antiphase: they are equal but opposite, and if added together
will sum to zero. If the phase difference is 90 degrees then the
signals are said to be in quadrature.
Phase difference and path difference
• If the phase difference between two waves is 2
then the path difference between that two waves is
.
• Let for a path difference x, the phase difference is
.
• We know that
for a path difference , phase difference = 2 
so, for path difference x, the phase difference = 2x
So, phase difference  =
2x


2


 path difference 
Angular frequency
angular frequency ω (also called angular speed) is a
scalar measure of rotation rate.
Angular frequency is a measure of how fast an object is rotating
• The period T of the motion is the time taken for
the particle to go through one full circle.
T = 2/
• Frequency f =1/T
What is light?
Electromagnetic radiation of any
wavelength.
The three basic dimensions of light :
•intensity (or amplitude, perceived by humans as the
brightness of the light),
•frequency (or wavelength, perceived by humans as the
color of the light),
•polarization (or angle of vibration and not perceptible
by humans under ordinary circumstances)
PRINCIPLE OF SUPERPOSITION
principle of superposition states that the net
displacement at a given place and time caused
by two or more waves traversing the same
space is the vector sum of the displacements
which would have been produced by the
individual waves separately.
Two wave pulses are travelling, one is moving to
the right, the other is moving to the left. They
pass through each other without being disturbed,
and the net displacement is the sum of the two
individual displacements.
COHERENT SOURCES
Sources emitting light waves of the same frequency,
nearly same amplitude and are always in phase with each
other or having a constant phase relationship between
them, means that two sources must emit radiations of the
same wavelength.
In practice it is not possible to get independent
Two sources which are coherent. But two
virtual Sources formed from one single source
can act as Coherent source.
Two ways to get coherent source
•Division of wave front : waves from two
sources are formed from a single source
Division of amplitude : waves from two sources
are formed from a single source due to reflection and
Refraction. One of these source is real other virtual
source
P
Virtual
source
Monochromatic
source
S1
S
S2
D
DIVSION OF WAVE FRONT
I
II
d
a
c
b
DIVISION OF AMPLITUDE
INTERFERENCE
Interference is the superposition of two or
more coherent waves resulting in a new
wave pattern.
There are two types of interference:
Constructive Interference
Destructive Interference
Conditions of Interference
•The interfering waves should be coherent
•The interfering waves must be of same
wavelengths
•Two waves must have the same state of
polarization to get fringes of maximum
contrast
Constructive and destructive interference
If the two waves have the same amplitude A and
wavelength the resultant waveform will have
amplitude between 0 and 2A depending on
whether the two waves are in phase or out of
phase.
If the two waves are in phase, interference will be
constructive.
If the two waves are out of phase, interference
will be destructive.
Two waves that are in phase,with amplitudes A1
and A2. Their troughs and peaks line up and the
resultant wave will have amplitude A = A1 + A2.
This is known as constructive interference.
If the two waves are 180° out of phase, then one
wave's crests will coincide with another wave's
troughs and so will tend to cancel out. The
resultant amplitude is A = |A1 − A2|. If A1 = A2
the resultant amplitude will be zero. This is
known as destructive interference.
combined
waveform
wave 1
wave 2
Two waves in phase
Two waves 180° out
of phase
P
S1
yn
d/2
d
O d/2
S2
D
Let y1 and y2 are the displacements
of two waves coming from
S1 and S2
L
y  a cost
1
y  a cost   
2
 is the phase difference between two waves reaching
At P from S1 and S2, a be the amplitude of wave.
y  y1  y2  a cos t  a cos(t   )
wt  wt  
wt  wt  
 2a cos
cos
2
2
 2a cos
2a cos 
2

2
cos( wt 

2
)
 amplitude of the resultant wave
I  4a cos
2
2
intensity
2
is square of amp litude
if   0,2 ,4 ,..2n
or p ath difference x  0,  ,2..n ;
I  4a ( maxima )
2
if    ,3 ,..( 2n  1)
 3 (2n  1)
p ath difference x 
,
..
;
2 2
2
I  0( minima )
In each case n = 0,1,2….
For incoherent light

I  4a cos
2
2
2
1
 4a   2a  ( a  a )
2
= sum of intensity
2
2
2
2
of constituent waves.
Interference of two circular waves - Wavelength (decreasing
bottom to top) and Wave centers distance (increasing to the
right). As time progresses, the wave fronts would move
outwards from the two centers, but the dark regions
(destructive interference) stay fixed.
Young’s Double slit experiment
Experiment consists of letting light passes through
two slits producing fringes on a screen. These
fringes or interference patterns have light and dark
regions corresponding to where the light waves
have constructively and destructively interfered.
(The experiment can also be performed with a
beam of electrons or atoms, showing similar
interference patterns.
THE INTERFERENCE FRINGES
P
S1
yn
d/2
d
O d/2
S2
D
At point P for maxima we must have
S2P – S1P = n, n = 0,1,2,3…
L
d 2
( S 2 P )  [ D  ( yn  ) ]
2
2
2
d 2
( S1P )  [ D  ( yn  ) ]
2
2
2
( S2 P)  ( S1P) 
2
2
d 2
d 2
2
[ D  ( yn  ) ]  [ D  ( yn  ) ]
2
2
2
 D  yn  yn d  D  yn  yn d
2
2
2
2
 2 yn d
thus, ( S 2 P )  ( S1 P )  2 yn d
2
2
2 yn d
( S 2 P )  ( S1 P ) 
( S 2 P )  ( S1 P )
If d<D then S2PS1PD and thus S2P+S1P=2D
2 yn d yn d
therefore, n 

2D
D
yn d
or , n 
D

n D
yn 
d

yn 
y1 
y2 
y3 
nD
d
D
d
2D
d
3D
d
Distance between any two consecutive bright fringes
2D D 3D 2D
y2  y1  y3  y2 



d
d
d
d
D
Similarly for dark fringes,

d

D S P  S P  (2n  1) 2 , n  0,1,2,3..
or, yn1  yn   
d
2
1
So we get, for dark and bright fringes
(2n  1)D
nD
yn 
; yn 
2d
d
(2n  1)D
nD
yn 
; yn 
2d
d
n  0,  y0 
D
2d
3D D
n  1,  y1 
;
2d d
5D 2D
n  2,  y2 
;
2d
d
y2
Fringe width
;0


5D
3D
D
 y1 


2d
2d
d
D
d
Fringe width
Seperation between dark and bright fringes
3 d
d

2d
d

d

2d
O is equidistant from S1 and S2 so light waves superposed
at O are in phase so light intensity at O will be maximum.
• At O we observe the central bright fringe. For this
fringe n=0 y = 0. so central bright fringe will be
referred as zeroth order bright fringe.
• At n=1 we have y= 1D/d, this is the first order
bright fringe.
• At n=0 we observe first dark fringe at y = D/2d.
So at n=0 we have the first order dark fringe.
Dark areas = Troughs (valleys)
Light aresa = Crests (peaks)