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Wave nature of light and optical instruments

Wave nature of light and optical instruments. Physics 123, Spring 2006. Diffraction. Single slit diffraction Angular half width of the first peak:. True limit of geometric optics. Aberrations limit resolution of mirrors and lenses (optical devices)

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Wave nature of light and optical instruments

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

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

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

  6. Resolution of a Human Eye • Diameter of the pupil: D=0.1-0.8 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) 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) 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 Lecture VII

  9. 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 Lecture VII

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

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