Transcript Diffraction - Happy Physics With Mineesh Gulati

Physics Lecture Resources
Prof. Mineesh Gulati
Head-Physics Wing
Happy Model Hr. Sec. School, Udhampur, J&K
Website: happyphysics.com
happyphysics.com
Ch 36 Diffraction
© 2005 Pearson Education
36.1 Fresnel and Fraunhofer Diffraction
Diffraction:
Effects occurs when light strikes a barrier that has
an aperture or an edge. The interference patterns
formed in such a situation.
Fresnel diffraction:
diffraction which occur when both point source
and the screen are relatively close to the obstacle.
Fraunhofer diffraction:
diffraction which occur when both point source
and the screen are far enough to the obstacle
© 2005 Pearson Education
36.2 Diffraction form a Single Slit
© 2005 Pearson Education
Horizontal slit
dark fringes in single-slit
diffraction
mλ
sin  
a
m
ym  x
( for ym  x)
(m a1 ,2,  3, ... )
© 2005 Pearson Education
Example 36.1
You pass 633 nm laser light through a narrow slit and
observe the diffraction pattern on a screen 6.0m away.
You find that the distance on the screen between the
centers of the first minima outside the central bright
fringe is 32mm. How wide is the slit?
ANS:
x (6.0m)(633  10 )
a

3
y1
(32  10 m) / 2
9
4
 2.4  10 m
 0.24mm
© 2005 Pearson Education
36.3 Intensity in the Single-Slit Pattern
© 2005 Pearson Education
Amplitude in single-slit diffraction
sin(  / 2)
E p  E0
 /2
intensity in single-slit diffraction
2

 sin[a(sin ) / λ] 
I  I0 

a(sin ) / λ 



2

a sin 
© 2005 Pearson Education
© 2005 Pearson Education
Intensity Maxima in the single-slit pattern
For a=λ
For a=5λ
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36.4 Multiple Slits
Constructive interference
d sinθ= mλ
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Phasor diagrams for
light passing through
eight narrow slits
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Interference pattern for N slits
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36.5 The Diffraction Grating
intensity maxima,
multiple slits
d sin   mλ
(m  0,  1,  2,  3, ... )
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Grating Spectrographs
Chromatic
resolving power

R

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36.6 X-Ray Diffraction
Which used to
verified that x-rays
are waves and the
atoms in a crystal
are arranged in a
regular pattern
© 2005 Pearson Education
© 2005 Pearson Education
Bragg condition for
constructive interference from
an array
2d sin   mλ
(m  1, 2, 3, ... )
© 2005 Pearson Education
© 2005 Pearson Education
36.7 Circular Apertures and Resolving Power
diffraction by a
circular aperture
λ
sin  1  1.22
D
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36.8 Holography
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Typical arrangement for hologram
Beam expander
Mirror 1
Laser
Mirror 3
Beam splitter
Film
Mirror 2
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Reconstruction
Laser
© 2005 Pearson Education
Diffraction occurs when light passes through an aperture or
around an edge. When the source and the observer are so far
away from the obstructing surface that the outgoing rays can be
considered parallel, it is called Fraunhofer diffraction. When the
source or the observer is relatively close to the obstructing
surface, it is Fresnel diffraction.
© 2005 Pearson Education
Monochromatic light sent through a narrow slit of
width a produces a diffraction pattern on a distant
screen. Equation (36.2) gives the condition for
destructive interference (a dark fringe) at a point P
in the pattern at angle θ . Equation (36.7) gives the
intensity in the pattern as a function of θ . (See
Examples 36.1 through 36.3)
© 2005 Pearson Education
A diffraction grating consists of a large number of thin parallel
slits, spaced a distance d apart. The condition for maximum
intensity in the interference pattern is the same as for the twosource pattern, but the maxima for the grating are very sharp
and narrow. (See Example 36.4)
© 2005 Pearson Education
A crystal serves as a three-dimensional diffraction grating for x
rays with wavelengths of the same order of magnitude as the
spacing between atoms in the crystal. For a set of crystal
planes spaced a distance d apart, constructive interference
occurs when the angles of incidence and scattering (measured
from the crystal planes) are equal and when the Bragg
condition [Eq.(36.16)] is satisfied. (See Examples 36.5)
© 2005 Pearson Education
The diffraction pattern from a circular aperture of diameter D
consists of a central bright spot, called the Airy disk, and a series
of concentric dark and bright rings. Equation (36.17) gives the
angular radius θ1 of the first dark ring, equal to the angular size of
the Airy disk. Diffraction sets the ultimate limit on resolution
(image sharpness) of optical instruments. According to Rayleigh’s
criterion, two point objects are just barely resolved when their
angular separation θis given by Eq. (36.17). (See Example 36.6)
© 2005 Pearson Education
END
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