Physics 103
April 10, 2017
Lecture 20
Discussion Session
Interference – Part 2 (Ch. 37)
Announcements
• Labs for this week have been cancelled.
– Labs will resume after Spring Break.
M. Afshar
2
Review of Optics Formulas
Mirror
Thin Lens
0 when center is in front (concave mirror).
0 when center is in back (convex mirror).
or
or
0 when center is in back.
0 when center is in front.
[Lens-makers’ formula]
1
0 ,
0 ,
0.
0.
[Thin lens formula]
0 when object is in front.
0 when object is in back.
0 when object is in front.
0 when object is in back.
0 when image is in front (real image).
0 when image is in back (virtual image).
0 when image is in back (real image).
0 when image is in front (virtual image).
≡
≡
0 when image is upright.
0 when image is inverted.
0 when image is upright.
0 when image is inverted.
A concave mirror can create an inverted real image
or an upright virtual image.
A convex mirror can create an upright virtual
image only.
A converging lens can create an inverted real
image or an upright virtual image.
A diverging lens can create an upright virtual
image only.
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Review of Optics Formulas
Refracting Surface
0 when center is in back (convex surface).
0 when center is in front (concave surface).
0 ,
0.
0 when object is in front.
0 when object is in back.
0 when image is in back (real image).
0 when image is in front (virtual image).
≡
0 when image is upright.
0 when image is inverted.
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Interference of 2-D Waves
• We wish to study the superposition of two identical
2-dimensional sinusoidal waves.
• For visible light in air:
• We will be interested in
much larger distances:
• Certain approximations will
facilitate calculations.
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Interference
• Superposition of two waves of equal amplitudes:
• When wavelengths and frequencies are also equal:
• When phase constants are also equal:
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Constructive and Destructive
• Constructive interference occurs when:
where
Interference Approximation
• Destructive interference occurs when:
where
Interference Approximation
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Interference Approximation I
• When
, the rays are almost parallel:
,
,
• When the rays are parallel, the path difference is:
,
sin
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Interference Approximation II
• Assume
. Expand
and
in
about
:
/
/
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Practice Problem
Two point sources, separated by
, emit
light with wavelength
. A screen is placed a
distance
away from the sources. Calculate
the coordinate of the first point of destructive
interference (1st intensity minimum) on the screen.
(for 1st minimum)
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One Point Source
• One point source illuminates a screen. What is
the intensity on the screen?
– As increases, distance to source increases, which
means intensity should decrease.
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Two Point Sources
• Two point sources illuminate a screen. What is
the intensity on the screen?
– The two sources interfere, resulting in alternating
maxima and minima.
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Two Point Sources (cont.)
• Intensity of two point sources:
• Where are the minima (destructive interference)?
• Where are the maxima (constructive interference)?
• How would you find the
coordinate?
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N Point Sources
•
point sources illuminate a screen. What is the
intensity on the screen?
(Six Point Sources)
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N Point Sources (cont.)
• Intensity of
point sources:
• Where are the minima (destructive interference)?
• Where are the maxima (constructive interference)?
• How would you find the
coordinate?
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15
Double-Slit Experiment
• How do you create two E&M waves with equal
amplitudes, wavelengths, frequencies and phase
constants?
Use a double-slit of course! Each slit becomes
Point source creates
spherical waves
Far from source,
spherical waves look
like plane waves
M. Afshar
a source of new
spherical waves!
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