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Unformatted text preview: PHYSICS 222
Introduction to Classical Physics II
Prof. Ruslan Prozorov
Iowa State University
Fall 2011 LECTURES 32
Diffraction.
Diffraction grating.
Limits of optical resolution. Fresnel and Fraunhofer diffraction
According to
geometric optics, a
light source shining
on an object in
front of a screen
will cast a sharp
shadow.
Surprisingly, this
does not occur. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 2 Light bends around the corner
Huygens’ model: each point in the wavefront emits a wavelet. obstacle
•
• Block the lower sources of induced fields with an obstacle
Induced fields from upper sources/wavelets are still spherical
– reach beyond blockage
– waves effectively “bend” around corners PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 3 Diffraction and Huygen’s Principle
• Diffraction patterns can be analyzed using Huygen’s Principle. Recall,
every source of a wave front can be considered to be the source of
secondary waves. Superposition of these waves results in diffraction. • If the source and the screen are close to the edge causing the diffraction,
the effect is called “nearfield” or Fresnel diffraction. If these objects are
far apart, so as to allow parallelray modeling, the diffraction is called
“farfield diffraction” or Fraunhofer diffraction. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 4 AM/FM radio
Examples: AM signal with f = 1000 kHz λ = 300 m FM signal with f = 100 MHz λ=3m In mountainous areas, AM radio station reception is much
better because AM waves are diffracted “around” the
mountain tops and into the valleys
FM waves propagate “in a straight line” and cannot reach
the valleys (unless an antenna on top of the mountain is
used) PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 5 Your roommate’s music
Like interference, diffraction applies to ALL waves (not just light) Human ear perceives f ~ 20 Hz – 20 kHz λ ~ 2 cm – 2 m A door left ajar (opening ~ 15 cm) protects you from most of
your roomie’s music, but not from the bass track. (same
applied to cars with ajar windows)
Also: That’s why all home theater speakers must be “in line of
sight”, but subwoofers can be behind the sofa. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 6 diffraction from a single slit PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 7 intensity in a singleslit pattern PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 8 dark fringes in singleslit diffraction PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 9 singleslit diffraction
Slit of width a
• consider it made of a large number of point sources
• interference by N sources
P N sources > N phasors θ
a
R >> a Angle between first and last phasors: PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University ka sin 2 a sin 9 November 2011 10 Length of the arc is NE0 = Emax
(amplitude when β = 0) r β/2
r β/2 EP E max
r (β in radians) From the triangle: β E0 EP 2r sin E max 2
sin
2 2 r E P E max sin 2 2
PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University EP
sin 2 2r E max 2 sin 2
IP I max 2 9 November 2011 11 Minima: 2m m 1, 2... a sin m m 1, 2... Maxima: ( I
I max ) b » 2m + 1 p sin 2 2 2 (and b = 0) θ This is the
“normal” part
PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University This is light
“bending around
the corner”!
9 November 2011 12 intensity maxima in a singleslit pattern PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 13 Fresnel or Fraunhofer limit? 2 a
F
x
F 1
F 1 Fresnel diffraction (nearfield diffraction) Fraunhofer diffraction (far – field diffraction)  diffraction pattern is viewed at a
long distance from the diffracting object, and also when it is viewed at the focal
plane of an imaging lens. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 14 Fraunhofer limit PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 15 example: Fraunhofer diffraction
=600 nm y1 x 16 mm a
600 109
a=6.0 0.255 mm
3
16 10
PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 16 diffraction and wavelength
Diffraction effects (= light bending around the corner) are
most important when a ~λ Diffraction pattern
of a square slit (with
both sides a ~λ) PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 17 rectangular slit PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 18 circular opening (Airy pattern) PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 19 Interference from multiple slits
• The approximation of sin θ = θ is very good
considering the size of the slit and the wavelength
of the light. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 20 Multiple slit interference
• The analysis of intensity to find
the maximum is done in similar
fashion as it was for a single slit. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 21 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 22 several slits interference PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 23 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 24 realistic doubleslit
We need to take diffraction into account!
Superposition of interference and diffraction effects:
Interference: Diffraction: The total output: IP Imax cos 2 2 sin 2
IP I max 2 2 d sin 2 2 sin 2 2
IP I max cos 2 2 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University a sin 2 9 November 2011 25 d
Two slit interference
MAXIMUM when sin m d Each slit diffraction
MINIMUM when sin m a a Interference pattern modulated
by diffraction pattern
(with d >>a ) PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 26 0
–1 1 –2 –3 (–5) –4 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 2 3 4
(5)
9 November 2011 27 the diffraction grating
Two slits change the intensity
profile of interference; many
slits arranged in parallel
fashion produce grating. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 28 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 29 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 30 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 31 PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 32 The grating spectrograph
A grating can be used like a prism, to disperse the
wavelengths of a light source. If the source is built of
discrete wavelengths, we have spectroscopy.
Chemical systems and astronomical entities have
discrete absorption or emission spectra that contain
clues to their identity and reactivity. PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 33 The grating spectrograph example PHYS222  Lecture 32  Prof. Ruslan Prozorov  Iowa State University 9 November 2011 34 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.
 Fall '09
 MEYER

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