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Chapter 38
Diffraction and Polarization
PHY 1371
Dr. Jie Zou
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Outline
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Introduction to diffraction
Diffraction from narrow slits
Resolution of single-slit and circular
apertures
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Dr. Jie Zou
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Introduction to diffraction
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Diffraction: Waves
bend or diffract, when
they pass by a barrier or
through an opening. The
divergence of light from
its initial line of travel is
called a diffraction.
Diffraction pattern
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Dr. Jie Zou
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Diffraction from narrow slits:
Observation
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Diffraction pattern
of a single slitobservation: The
pattern consists of a
central bright fringe
flanked by much
weaker maxima
alternating with dark
fringes.
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Diffraction of narrow slits:
Explanation
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PHY 1371
Explanation: According to
Huygens’s principle, each
portion of the slit acts as a
point source of light waves.
Light from one portion of the
slit can interfere with light
from another portion, and the
resultant light intensity on a
viewing screen depends on
the direction .
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Dependence of the resultant
light intensity on direction 
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Assumption: The viewing
screen is very far from the
single slit.
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Large number of small zones, each
with a width y.
Phase difference between adjacent
zones:
 = (2/)y sin
Total electric filed E at point P: EP =
Esin(t) + Esin(t+) +…+
Esin(t+N)
It can be shown that:
EP =(NE)[sin(/2)/(/2)]sin(t+),
where  = N  = (2/) a sin.
Light intensity at P:
I = Imax [sin(/2)/(/2)]2.
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Light intensity vs. /2 plot
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PHY 1371
For a single-slit diffraction,
most of the light intensity is
concentrated in the central
bright fringe.
Condition for intensity
minima: sin  = m(/a), m
= 1, 2,…
The central maximum
occurs at  = 0 (central
point on the screen).
To a good approximation,
the secondary maxima lie
midway between the zero
points: /2 =3/2, 5/2,…
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Example 38.2 Relative
intensities of the maxima
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Find the ratio of the intensities of the
secondary maxima to the intensity of
the central maximum for the single-slit
diffraction pattern.
PHY 1371
Dr. Jie Zou
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Resolution of single-slit and
circular apertures
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The ability of optical systems to distinguish
between closely spaced objects is limited
because of the wave nature of light.
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Rayleigh’s criterion for
resolution
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Dr. Jie Zou
Rayleigh’s criterion:
When the central
maximum of one image
falls on the first
minimum of the other
image, the images are
said to be just resolved.
For a slit with width a,
the limiting angle of
resolution is: min = /a.
For a circular aperture
of diameter D, the
limiting angle of
resolution is:
min = 1.22(/D).
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Example 38.5 Resolution of
the eye
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Estimate the limiting
angle of resolution for
the human eye,
assuming its resolution
is limited only by
diffraction (Choose  =
500 nm, and pupil
diameter = 2 mm)
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Homework
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Ch. 38, P. 1238, Problems: #1, 2, 18.
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Dr. Jie Zou
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