diffraction ibh uem kolkata 2015 (1)
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DIFFRACTION OF LIGHT
Indrani Bhattacharya
MODULE 2 : OPTICS 1
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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Diffraction of light: Fresnel and Fraunhofer class. Fraunhofer diffraction for single slit and double
slits. Intensity distribution of N-slits and plane
transmission grating (No deduction of theintensity distributionsfor N-slits is necessary), Missing orders.
Rayleigh criterion, Resolving power of grating andmicroscope(Definition and formulae)
TOPICS TO BE COVERED
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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DEFINITION
The slight bending of light round the edge of an object , whose size is comparable with the wavelength of light, and spreading the same into the regions of the geometric shadow is called the Diffraction of light.
The light waves are diffracted only when the size of the obstacle is com--parable to the wavelength of light.
If the opening is much larger than the light's wavelength, the bending will be almost unnoticeable.
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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What is the Difference between INTERFERENCE & DIFFRACTION ?
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DIFFERENT TYPES OF DIFFRACTION PHENOMENA
FRESNEL TYPE
FRAUNHOFFER TYPE
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FRESNEL DIFFRACTION PHENOMENON
The Fresnel diffraction deals with the near-field diffraction, wherethe Source , the Screen or both are at finite distances from the obstacle and the distances are important.
In Fresnel diffraction, the incident wavefront is either Spherical orCylindrical.
In Fresnel Diffraction, the centre of diffraction may be bright or darkdepending upon the number of Fresnels Zone.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FRAUNHOFER DIFFRACTION PHENOMENON
The Fraunhofer diffraction deals with the far-field diffraction, wherethe Source , the Screen or both are at infinite distances from theobstacle; it is viewed at the focal plane of an imaging lens.here, the inclination is important.
In Fraunhofer diffraction, the incident wavefront is Plane.
In Fraunhofer Diffraction, the centre of diffraction pattern is always bright.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Computer simulation of Fraunhofer diffraction by a rectangular aperture
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Computer simulation of the Airy diffraction pattern, of Circular Aperture
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FRAUNHOFER DIFFRACTION DUE TO SINGLE SLIT
Concept of a Single Slit :
A slit is a rectangular aperture whose length is as large compared to itsbreadth.
The Width of the Slit is comparable to the Wavelength of light used.
Theory / Principle
The study of Diffraction pattern is based upon the superposition of Huygens secondary wavelet which are supposed to be generated atevery point on the wavefront of the slit.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
i
A
B
dx
O
C
E F P
Single Slit
Lens
Plane ofObservation
Figure 3 : Showing experimental arrangement of Fraunhofer DiffractionPattern through Single Slit.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
AB is a long narrow slit of width = a, placed perpendicular to theplane of paper and is illuminated by a parallel beam of monochro--matic light of wavelength .
The figure shows the cross-section of the slit.
O is the centre of the slit.
Let i be the angle of incidence with the normal to the plane of theslit.
Due to Diffraction, the rays will generate secondary wavelets in all possible directions and are focussed on the Focal Plane of theConverging Lens L.
Parallel Diffracted Rays will be focussed by the lens on the screenat P to form the image of the Slit.
SALIENT POINTS ABOUT THE EXPERIMENTAL SET UP
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
SALIENT POINTS ABOUT THE EXPERIMENTAL SET UP
The Point of Observation is at INFINITY, and obviously, it is a case of Fraunhofer Class of Diffraction.
Let us consider a diffrcating element of width, dx at C at a distance xfrom O.
OE and OF are two Perpendiculars drawn on the Incident and the Diffracted rays ; hence, OE and OF will represent Incident and Diffracted Wavefronts.
We will be finding out the expression for the Intensity of Light at P.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
The equation of Vibration on the Incident Wavefront OE can be represented by :
where c is the velocity of Light.
The equation of Vibration on the Diffracted Wavefront OF can be represented by :
)1...(2
cti
Aey
)2....()(
2ECFcti
Aey
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
But we can write :
which means :
Hence, eqn (2) reduces to :
sinsin xixCFECECF
)3.....(sinsin xixECF
)4....()(
2
xcti
Aey
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
Neglecting the effects of disturbance due to inclination and others, the disturbance at P due to element dx at C is given by :
Hence, the Total Disturbance at P due to the whole Slit is given by :
)5.....()(
2
dxAeydxdsxcti
2/
2/
22
2/
2/
)(2
a
a
xicti
a
a
xcti
dxeAeS
dxAeydxdsS
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
)6.....(2
2
2
2
i
ee
a
AaeS
i
eeAeS
ai
aicti
ai
aicti
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
Substituting
we have from previous expression :
Xa
X
XAaeS
i
ee
X
AaeS
cti
iXiXcti
sin
2
2
2
)7....(sin
2cti
eX
XAaS
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
)7....(sin
2cti
eX
XAaS
Examining expression (7) , it appears that the Vibration is truly Simple Harmonic.
The Intensity at P is proportional to the Square of Amplitude, i.e.,
Let us choose the Constant of Proportionality as Unity, i.e.,
)8....(22
SKISI
1K
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
Hence, the Intensity at P will be :
)9...(sinsin
2
222
2
X
XaA
X
XAaI
)10...(
sinsin
sinsinsin
2
2
22
ia
ia
aAI
2
2
22
2
2
22
sinsin
sinsinsinsin
ia
ia
aAa
a
aAI
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
)9...(sinsin
2
222
2
X
XaA
X
XAaI
)11...(sin2cossin2
2.sincossin2.
3
222
4
2222
X
XXXXaA
dX
dI
X
XXXXXaA
dX
dI
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
From eqn.(10), we can explore the condition of Maxima and Minima by putting :
which implies :
)12...(0dX
dI
0sin
2
222
X
XaA
dX
d
)13...(0
sincossin2
3
22
X
XXXXaA
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
)14...(0
sincossin2
3
22
X
XXXXaA
We have as conditions :
)...(aX
)...(0sin bX
)...(0sincos cXXX
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
From condition (a), we have :
which must be true, when ;
But since , this condition is invalid and we reject this one.
From condition (b), we have :
which means :
aX
0
0
0sin X
)15....(
sin0sin
a
nn
a
na
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
If we find and put the condition in eqn. (15), we can find that :
This gives the Condition for Minimum and the other successive minima are given by :
From eqn. (16) it is apparent that, the Minima are Equidistant.
2
2
dX
Id
02
2
dX
Id
)16,....(3
,2
, 321aaa
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
From condition (c) we have :
Condition (c) gives the condition for maxima.
The value of X satisfying the eqn. (c) is obtained by drawing two curves :
(i) Y =X & (ii) Y = tan X on the same scale.
)'....(tancos
sin
)...(0sincos
cXXX
X
cXXX
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
The Point of Intersection of the two curves will give the values of X, satisfying the equation tan X = X, the maximum value of intensity will occur at :
which is Central Band.
gives the next value of the Intensity :
with
)17...(sin
0 222
222
000
0
aAX
XaALtIX
X
43.11 X
22
1 0469.0 aAI )18....(43.11 a
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
gives
with
gives
with
46.22 X22
2 0168.0 aAI
)19....(46.22a
47.33 X22
3 0083.0 aAI
)20....(47.33a
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XY
Y = X
X
Intensity
0 2 3--2-3
Y= t
anX
1.4
3
2.4
6
3.4
7
-1.4
3
-2.4
6
-3.4
7
Plotting of Intensity distributionsDue to single slit
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
Expressions (17 ), (18 ), (19 ) and (20) represent that :
The diffraction pattern consists of a Bright Central Maximum with Intensity represented by .
The central maximum is followed by minimum of Zero Intensity.
The minimum of Zero Intensity is followed by secondary maximum of intensity at at both sides of the centralmaxima.
It is also apparent from the graph is that the maxima are NOT equidistant at lower orders.
0I
43.11 X1I
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
The angle of Diffraction, for the first minimum on either side of the Central Maximum is given by :
The Condition for Minima is given by :
For Normal Incidence : i = 0;
Therefore : ;
For First Order Minima, we have, n=1 for .
1
)15....(a
n
a
ni
sinsin
a
n sin
1
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
DERIVATION OF THE EXPRESSION FOR INTENSITY AT P
CONDITIONS FOR MAXIMA AND MINIMA
a
1sin
For First Order Minima, we have, n=1 for .
Since is small,
Hence, the Angular Width of the Principal Maxima, i.e., is given by :
i.e., inversely proportional to the Width of the Slit.
1
1 11sin
a
1
12
a
22 1
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FRAUNHOFER DIFFRACTION DUE TO DOUBLE SLIT
Concept of Double Slit :
Double slit is an arrangement where two single slits are placed in parallelon the same plane
The Width of each Slit is generally identical and much smaller than their lengths.
The slits have an opaque space between them.
The widths of both the slits and Opaque Space should be of the order ofwavelength used.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Figure shows Same double-slit assembly (0.7 mm between slits); in topimage, one slit is closed. In the single-slit image, a diffractionpattern (the faint spots on either side of the main band) forms due tothe nonzero width of the slit. A diffraction pattern is also seen in thedouble-slit image, but at twice the intensity and with the addition ofmany smaller interference fringes.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FRAUNHOFER DIFFRACTION DUE TO DOUBLE SLIT
Theory / Principle
The study of Diffraction pattern due to Double Slits consists of diffractionfringes caused by rays diffracted from both slits superposed on the
interference fringes caused by rays coming from each pair of correspondingpoints on the two slits.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Figure showing double-slit diffraction pattern by a plane wave
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
a
b
aP
d
1S
2S
O
1O
i A P B
x
dx
Figure showing Fraunhofer diffraction thru. Double slits MN and RS
Lens
Plane ofObservation
N
M
S
R
MN
RS
Slit 1
Slit 2
21SS Plane of theSlita/2
a/2
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
SALIENT POINTS ABOUT THE EXPERIMENTAL SET UP
represents the section of the slit.
a is the width of each slit and b is the width of the opaque space.
and are the mid-points of the slits MN and RS respectively.
The distance between and is d which is equal to (a+b).
is the angle of incidence.
The rays will be diffracted at all possible directions. Let us considera beam of rays for which the angle of diffraction is .
L is the Converging lens which focuses the diffracted rays on its focalplane.
As the Source and Point of Observation both are effectively at Infinity,obviously, it is a case of Fraunhofer class of diffraction.
21SS
O
1OO
i
'O
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
2S
1O
A P B
x
dx
a
i
To find the Intensity on the screen, let us consider a diffracting elementof width dx at P where .
From let us draw two perpendiculars and on the incident and diffracted rays.
xPO 1
1O BO1AO1
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
2S
1O
A P B
x
dx
a
i
Let the equation of vibration of the incident wavefront is representedby :
where A is the amplitude of the wave and is the wavelength. BO1
AO1
)1...(2
cti
Aey
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
2S
1O
A P B
x
dx
a
i
Let the equation of vibration of the diffracted wavefront is representedby :
BO1
)2...(
2APBcti
Aey
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
2S
1O
A P B
x
dx
a
i
Now,
where :
)3...()sin(sin
sinsin
xixAPB
xixPBAPAPB
)4...(sinsin i
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
Expression (2) reduces to:
)5...(
2
xcti
Aey
2S
1O
A P B
x
dx
a
i
Lens
Plane ofObservation
1P
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ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
2S
1O
A P B
x
dx
a
i
Lens
Plane ofObservation
1P
The disturbance at due to element dx at P is given by :
)6.....()(
2
dxAeydxdsxcti
1P
S
R
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
)7...(
2/
2/
22
1
2/
2/
)(2
111
a
a
xicti
a
a
xcti
dxeAeS
dxAedxydsS
The disturbance at due to the entire slit is given by :
The disturbance at due to the other slit is :
1P
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
RS
MN1P
)8...(
2/
2/
22
2
ad
ad
xicti
dxeAeS
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
Hence, the disturbance due to both the slits at will be : 1P
dia
a
xicti
ad
ad
xia
a
xicti
edxeAeS
dxedxeAeSSS
22/
2/
22
2/
2/
22/
2/
22
21
1
di
a
a
xicti
e
i
eAeS
2
2/
2/
22
12
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
Rearranging we can write :
diaiai
cti
ei
ee
a
AeS
2//
2
12
Let us put : Xa
)10...(2
sin2
cos1sin
12
2
22
didX
XAaeS
ei
ee
X
AaeS
cti
diiXiX
cti
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
Hence, the Effective amplitude of Vibration at due to two slits is :
The resultant Intensity is Proportional to the square modulus of amplitude.
Let the Constant of Proportionality is equal to 1.
Hence, the Intensity at is given by ::
1P
)11...(2
sin2
cos1sin
.
did
X
XAaAmp
1P
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
dX
XaAI
dX
XaAI
ddX
XaAI
2cos1
sin2
2cos22
sin
2sin
2cos1
sin
2
222
2
222
2
2
2
222
d
X
XaAI 2
2
222 cos2.
sin2
)12...(cossin
4 22
222
d
X
XaAI
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
)12...(cossin
4 22
222
d
X
XaAI
Substituting , we can write :
dY
)13...(cossin
4 22
2
0 YX
XII
Where : )14...(220 aAI
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
)13...(cossin
4 22
2
0 YX
XII
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
Upon examining eqn. (13), it is predominant that the factor arises due to the Single Slit Pattern.
The next factor arises due to the Disturbance coming from
the two slits having a Phase Difference .
Hence, the Minimum Intensity of Interference occurs when :
d2cos
2
2sin
X
X
d
2
2)12cos(0cos2
n
d
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
ANALYTICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
CONDITION FOR MINIMA
2
)12(sinsin
sinsin,
2)12(
2)12cos(0cos2
nbai
ibad
nd
nd
For Normal Incidence, i=0; hence ::
)14...(2
)12(sin
2)12(sin
ba
nnba
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
CONDITION FOR MINIMA
)14...(
2
)12(sin
ba
n
Successive minima are obtained for different values of n e.g.,
;..
2
7,3;
2
5,2
;2
3,1;
2,0
ban
ban
ban
ban
It is apparent the minima are equidistant; the distances between the successive minima are equal and is
ba
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
CONDITION FOR MAXIMA
For maxima, the condition will be :
,....2,1,0,sin)(
cos1cos2
nnba
nd
nd
,sinsinsin&
i
bad
for normal incidence, where i=0
)15....()(
sinba
n
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
CONDITION FOR MAXIMA
)15....()(
sinba
n
The Successive maxima are obtained for different values of n e.g.,
,.....)(
3,
)(
2,
)( bababa
This shows that the maxima are equidistant and is ba
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
)13...(cossin
4 22
2
0
d
X
XII
GRAPHICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
The term is called Interference term which gives a set of
equidistant dark and bright fringes as in the Youngs double slit interferenceexperiment.
The term is called Diffraction Term having a central maxima
at X=0, i.e., in the direction = 0.
The Maxima also occurs at values of X at : which
are called Secondary Diffraction Maxima.
d2cos
2
2sin
X
X
,....2
5,
2
3
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
GRAPHICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
)13...(cossin
4 22
2
0
d
X
XII
The minima are obtained when :
Which means :
That is :
for normal incidence, i=0.
except 0.
)15...(0sin
2
2
X
X
mX
mX
sin0sin
,...3,2,1,sin
,sin
mma
ma
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
GRAPHICAL STUDY OF INTENSITY OF DOUBLE SLIT DIFFRACTION PATTERN
)16,......(3,2,1,sin mma
This Minima are known as Diffraction Minima.
The Diffraction Pattern consists of a Central Maxima in the direction =0with alternate minima and secondary maxima of diminishing intensity oneither side.
The resultant Intensity distribution against angular position, is shown in figure.
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Figure showing DOUBLE SLIT Interference Pattern
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
Figure showing SINGLE SLIT Diffraction Pattern
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
FIGURE SHOWING DOUBLE SLIT DIFFRACTION PATTERN
(In Radians)
INTENSITY
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015
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UEM, B. Tech., 1ST YEAR, MODULE 2, OPTICS 1, 2015