Wave nature of light and optical instruments Physics 123, Spring 2006 11/23/2018 Lecture VII

Diffraction Single slit diffraction Angular half width of the first peak: 11/23/2018 Lecture VII

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) 11/23/2018 Lecture VII

Rayleigh criterion For a circular hole diameter D the resolution q=1.22l/D Note q∞ as D0 !!! – diffractive paradox 11/23/2018 Lecture VII

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 11/23/2018 Lecture VII

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) 11/23/2018 Lecture VII

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) 11/23/2018 Lecture VII

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 11/23/2018 Lecture VII

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 11/23/2018 Lecture VII

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 11/23/2018 Lecture VII