Lecture 16 Diffraction Chp. 37

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Lecture 16 Diffraction Chp. 37

• Topics
• Youngs double slit interference experiment
• Diffraction and the wave theory
• Single slit diffraction
• Intensity of single slit diffraction
• Circular aperture and double slit diffraction
• Diffraction grating
• Dispersion and resolving power
• Warm-up problem
• Demos
• Diffraction grating and slits
• Inverted mirage
• Measuring diameter of a strand Debras hair

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Youngs Double SlitInterference Experiment
m2
y
m1
q
m0
m1
m2
D
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Maxima
Minima
m ym /-
0 1 2 3 0 Dl/d 2Dl/d 3Dl/d
m ym /-
0 1 2 3 Dl/2d 3Dl/2d 5Dl/2d 7Dl/2d
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What about the intensity of light along the
screen?
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13E Suppose that Youngs experiment is performed
with blue-green light of 500 nm. The slits are
1.2mm apart, and the viewing screen is 5.4 m from
the slits. How far apart the bright fringes?
From the table on the previous slide we see that
the separation between bright fringes is
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Diffraction of a single slit
Find minimum
ym
Find maximum
First maximum lies on the axis at q 0 or ym0.
Other maxima lie in between the minima. To find
them we need to find the intensity along the
screen.
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Intensity of single slit diffraction
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Maxima/Minima conditions
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Exact solution for maxima
To find maxima of a function, take derivative
and set equal to 0
Transcendental equation. Solve graphically
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8. A 0.10-mm-wide slit is illuminated by light of
wavelength 589nm. Consider a point P on a viewing
screen on which the diffraction patters of the
slit is viewed the point is at 30o from the
central axis of the slit. What is the phase
difference between the Huygens wavelets arriving
at point P from the top and midpoint of the slit?
(Hint see Eq. 37-4.)
We note that nm 10-9 m 10-6 mm. From Eq. 37-4,
This is equivalent to 266.7 - 84? 2.8 rad 160o
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6. Sound waves with frequency 3000 Hz and speed
343 m/s diffract through a rectangular opening of
a speaker cabinet and into a large auditorium.
The opening, which has a horizontal width of 30.0
cm, faces a wall 100 m away. Where along that
wall will a listener be at the first diffraction
minimum and thus have difficult hearing the
sound? (Neglect reflections).
q
y
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Diffraction and Interference by a double slit
I I (double slit interference) x I(diffraction)
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Sample problem 37-4

• How many bright interference fringes fall within
  the central
• peak of the diffraction envelope?

The idea here is to find the angle where the
first minimum occurs of the diffraction
envelope.
Given
We have m0 and m1,2,3 and 4 on both sides
of central peak.
Ans is 9
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Diffraction by a circular aperature
The first minimum for the diffraction of light
from a circular aperature is given by
where d is the diameter of the aperature.
Our ability to resolve two distant point like
objects is determined when the first minimum of
one objects diffraction pattern overlaps the
central maximum of another. This is called
Raleighs criterion.
Example
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Example 15E. The two headlights of an approaching
automobile are 1.4 m apart. Assume the pupil
diameter is 5.0 mm and the wavelength of light is
550 nm. (a) At what angular distance will the
eye resolve them and (b) at what distance?
(a)
(b)
s
D
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Diffraction Grating
Double slit -- N slits or rulings.
w
d w/N
where w is the entire width of the grating
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Can be used to measure wavelength of light
Measure angles of diffracted lines with a
spectroscope using formula below. Then relate to
wavelength
Resolving power of grating. Measure of the
narrowness of lines
Highest R
Highest D
Dispersion of a grating. Measure of how well
lines are separated
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Show diffraction gratings with increasing N and
single slit diffraction with varying slit width a.
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Babinets Complementarity Principle
In the diffraction region the intensity is the
same whether you have an aperature or opaque
disk. You can also replace a slit with a wire or
hair strand. A compact disk is an example of a
diffraction grating in reflection instead of
transmission.
Experiment Measure diameter of a strand of hair
from Debra.
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Mirage
eye
sky
1,09
1.09
1.08
1.08
1.07
1.07
1.06
Hot road causes gradient in the index of
refraction that increases as you increase the
distance from the road
In the demo before you the gradient is in the
opposite direction
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Warm-up
HRW6 37.CQ.02. 73994 You are conducting a
single-slit diffraction experiment with light of
wavelength l. (a) What appears, on a
distant viewing screen, at a point at which the
top and bottom rays through the slit
have a path length difference equal to 5l.?
the m 5 maximum the m 5 minimum
the m 4 minimum the m 4
maximum (b) What appears, on a distant
viewing screen, at a point at which the top and
bottom rays through the slit have a path
length difference equal to 4.5l.? the
minimum between the m 4 and m 5 minima
the minimum between the m 4 and m 5 maxima
the maximum between the m 4 and m 5
maxima the maximum between the m 4 and
m 5 minima