Wave nature of light and optical
instruments
Physics 123, Spring 2006
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Lecture VII
1
Diffraction
• Single slit diffraction
• Angular half width of the
first peak:
sin  
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
D
Lecture VII
2
True limit of geometric optics
• Aberrations limit resolution of mirrors and lenses
(optical devices)
– This can be cured with careful manufacturing
(parabolic mirrors, etc)
• Diffraction is a true limitation of geometric
devices, objects must be >> wavelength (500nm)
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Lecture VII
3
Rayleigh criterion
• For a circular hole diameter D the resolution
=1.22/D
• Note ∞ as D0 !!! – diffractive paradox
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Lecture VII
4
Resolution of astronomic telescope
• How far can a star the size of the Sun (14x108m)be
resolved by a space telescope D=5.1m in =550
nm? (note that large D helps resolution)
=1.22/D= 1.22x550x10-9/5.1=1.3x10-7
distance=size/=14x108m/1.3x10-7~1016m~1 light
year
The nearest star – Proxima Centauri – 4.3 ly away
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Lecture VII
5
Resolution of a Human Eye
• Diameter of the pupil:
D=0.1-0.8 cm
• Wavelength =550nm
• Diffractive limit:
=1.22/D=8x10-5 to 6x10-4 rad
• Spherical aberration limit
5x10-4 rad
• Objects separated by 1 cm at a distance of 20 m
• At near point resolve two objects 0.1 mm apart
• Best microscope resolve objects 200 nm apart
• Useful magnification 500x (1000x to reduce eye strain)
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Lecture VII
6
Michelson Interferometer
• Use interference for
precise distance
measurement
• Beam splitter mirror –
observe interference –
dark vs bright spots –
resolution to /4
~100nm
• Used to catch
gravitational waves
(LIGO experiment)
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Lecture VII
7
Spectroscopy
•
•
•
•
Spectral lines – unique fingerprint of different elements
Use spectral line to analyze chemical composition.
Emission spectrum and absorption spectrum
Know chemical composition of remote stars by
analyzing their spectral lines
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Lecture VII
8
X-rays
• In 1895 W. C. Roentgen discovered that
• electrons accelerated by 30-150 kV in cathode tube
produce new type of radiation when they strike the glass
surface (or metal)
• This radiation exposes photographic film –
• X-ray photographs
• Neutral – do not change direction in electric or magnetic
film
• Does not exhibit diffractive pattern on narrow slits
• Light but very small wavelength
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Lecture VII
9
Diffractive pattern on crystals
• Atoms in crystals form
diffractive grating for
X-rays =10-2-10 nm
• Braggs equation:
m=2dsinf, m=1,2,3…
• Diffraction of X-rays is
used to study complex
molecules, e.g. DNA
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Lecture VII
10