LAST DANCE
CHAPTER 26 – DIFFRACTION – PART II
Instructor
Course
What’s Going On??
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Today – Finish (?) Diffraction
Tuesday – Nothing – No room is available for a review
session.
Wednesday – Examination #4 – Material that we
covered in chapters 24, 25 and 26.
Friday – Complete semester’s material. Start Review
Next Monday – Wrap-up and overview of the course.
December 12 - SATURDAY – 9:00AM – Psychology
Building Room PSY 108. BE THERE!!!
Last Mastering Physics Assignment Posted. No more!
Ever!
Last Time – Two Slit Interference
d sin  m
From another world .. sound.
Two small loudspeakers that are 5.50 m apart are emitting sound
in phase. From both of them, you hear a singer singing C#
(frequency 277 Hz), while the speed of sound in the room is 340
m/s. Assuming that you are rather far from these speakers, if you
start out at point P equidistant from both of them and walk
around the room in front of them, at what angles (measured
relative to the line from P to the midpoint between the speakers)
will you hear the sound (a) maximally enhanced? Neglect any
reflections from the walls.
v  340 m/s
f=277Hz
v 340
= 
 1.23m
f 277
d sin   m
m
sin  
d
Table
m
sin()=m/d

0
0
0
1
0.223636364
0.225544
13.26728
2
0.447272727
0.463714
27.27728
3
0.670909091
0.735434
43.26083
4
0.894545455
1.107413
65.14195
5
1.118181818
?
-
6
1.341818182
?
-
degrees
Diffraction
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Huygens’ principle requires
that the waves spread out
after they pass through
narrow slits
This spreading out of light
from its initial line of travel is
called diffraction

In general, diffraction occurs
when waves pass through small
openings, around obstacles or
by sharp edges
Diffraction Grating
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The diffracting grating consists of many equally
spaced parallel slits of width d
A
typical grating contains several thousand lines per
centimeter
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The intensity of the pattern on the screen is the result
of the combined effects of interference and
diffraction
Diffraction Grating
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The condition for maxima is
 d sin θbright = m λ
m = 0, 1, 2, …
The integer m is the order number
of the diffraction pattern
If the incident radiation contains
several wavelengths, each
wavelength deviates through a
specific angle
Diffraction Grating, 3
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All the wavelengths are focused at
m=0
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This is called the zeroth order
maximum
The first order maximum
corresponds to m = 1
Note the sharpness of the principle
maxima and the broad range of
the dark area

This is in contrast to the broad,
bright fringes characteristic of the
two-slit interference pattern
Active Figure: The Diffraction Grating
DIFFRACTION GRATING PATTERN
CD=Diffraction Grating
A shadow isn’t simply a shadow.
But what about this???
What about shadows???
Bright Center
Fringes
Shadow of a small steel ball
Reality
This effect is called DIFFRACTION
Diffraction Vs. Interference
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Both involve addition of waves from different places
and technically, both are the same phenomenon.
Observation requires monochromatic light and a small,
coherent light source.
If you are
close to a source (non paraxial approx) we call it Fresnel
Diffraction or near-field diffraction.
 Far away we call it Fraunhofer or far-field diffraction

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Diffraction usually refers to a continuous source of
wavelets adding up. Interference has a finite number
of sources for which the phase is constant over each
“source”.
Another case -
Geometrical
Shadow
Adding waves a piece at a time..
Maxima
D
Single Slit

Screen
WHY?
Single-Slit Diffraction
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A single slit placed between a distant
light source and a screen produces a
diffraction pattern
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It will have a broad, intense central band –
central maximum
The central band will be flanked by a series of
narrower, less intense secondary bands –
secondary maxima
The central band will also be flanked by a
series of dark bands – minima
The results of the single slit cannot be
explained by geometric optics
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Geometric optics would say that light rays
traveling in straight lines should cast a sharp
image of the slit on the screen
Single-Slit Diffraction
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Fraunhofer Diffraction occurs
when the rays leave the
diffracting object in parallel
directions
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Screen very far from the slit
Converging lens (shown)
A bright fringe is seen along the
axis (θ = 0) with alternating
bright and dark fringes on each
side
Single-Slit Diffraction
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According to Huygens’ principle, each
portion of the slit acts as a source of
waves
The light from one portion of the slit can
interfere with light from another portion
All the waves that originate at the slit
are in phase
Wave 1 travels farther than wave 3 by
an amount equal to the path difference
δ = (a/2) sin θ
Similarly, wave 3 travels farther than
wave 5 by an amount equal to the path
difference δ = (a/2) sin θ
Single-Slit Diffraction
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If the path difference δ is exactly a half wavelength,
the two waves cancel each other and destructive
interference results
δ = ½ λ = (a/2) sin θ  sin θ = λ / a
In general, destructive interference occurs for a single
slit of width a when
sin θdark = mλ / a
m = 1, 2, 3, …
Single-Slit Diffraction
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
A broad central bright fringe
is flanked by much weaker
bright fringes alternating
with dark fringes
The points of constructive
interference lie
approximately halfway
between the dark fringes
ym = L tan θdark , where sin θdark = mλ / a
25.
•A beam of laser light of
wavelength 632.8 nm falls on a thin slit
0.00375 mm wide. After the light passes
through the slit, at what angles relative
to the original direction of the beam is it
completely cancelled when viewed far
from the slit?
27.
•Parallel light rays with a
wavelength of 600 nm fall on a single slit.
On a screen 3.00 m away, the distance
between the first dark fringes on either
side of the central maximum is 4.50 mm.
What is the width of the slit?
30. •Light of wavelength 633 nm
from a distant source is incident on a slit
0.750 mm wide, and the resulting
diffraction pattern is observed on a
screen 3.50 m away. What is the
distance between the two dark fringes
on either side of the central bright
fringe?
35.
•A laser beam of wavelength
600.0 nm is incident normally on a
transmission grating having 400.0
lines/mm. Find the angles of deviation
in the first, second, and third orders of
bright spots.
38. •(a) What is the wavelength of light
that is deviated in the first order through
an angle of 18.0° by a transmission
grating having 6000 lines/cm? (b) What
is the second-order deviation for this
wavelength? Assume normal incidence.
END