1. Wave nature of light and optical instruments
Physics 123, Spring 2006
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Lecture VII

2. Diffraction Single slit diffraction
Angular half width of the first peak:
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Lecture VII

3. 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

4. Rayleigh criterion
For a circular hole diameter D the resolution q=1.22l/D
Note q∞ as D0 !!! – diffractive paradox
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Lecture VII

5. 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 l=550 nm? (note that large D helps resolution)
q=1.22l/D= 1.22x550x10-9/5.1=1.3x10-7
distance=size/q=14x108m/1.3x10-7~1016m~1 light year
The nearest star – Proxima Centauri – 4.3 ly away
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Lecture VII

6. Resolution of a Human Eye
Diameter of the pupil:
D= cm
Wavelength l=550nm
Diffractive limit:
q=1.22l/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

7. Michelson Interferometer
Use interference for precise distance measurement
Beam splitter mirror – observe interference – dark vs bright spots – resolution to l/4 ~100nm
Used to catch gravitational waves (LIGO experiment)
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Lecture VII

8. 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

9. X-rays In 1895 W. C. Roentgen discovered that
electrons accelerated by 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

10. Diffractive pattern on crystals
Atoms in crystals form diffractive grating for X-rays l= nm
Braggs equation:
ml=2dsinf, m=1,2,3…
Diffraction of X-rays is used to study complex molecules, e.g. DNA
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Lecture VII