interfere - Interference two-beam interference Young's...

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imaging Waves and Optics 1 Interference two-beam interference Young’s experiment Michelson interferometer thin film interference Fabry-Perot interferometer imaging Waves and Optics 2 Interference equal amplitudes phase difference intensity maximum intensity minimum intensity ( ) ( ) ( ) ( ) δ δ ω δ ω δ ω i t r k i t r k i t r k i e e E e E e E E + = + = + + 1 1 1 2 2 1 1 0 0 0 r r r r r r ( ) 2 / cos 4 2 0 δ I I = ( ) 1 2 1 2 δ δ δ + = r k k r r r 0 4 2 I I m = = π δ ( ) 0 1 2 = + = I m π δ
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imaging Waves and Optics 3 Two-beam Interference plane waves with different direction phase difference fringe separation can be much larger than wavelength θ =180° Æ l = λ /2 (standing waves) ( ) 2 / sin 2 2 θ λ π = = l kl ( ) 2 / sin 2 1 2 θ δ δ δ k k r k = + = r r θ 1 k r 2 k r 1 k r 2 k r imaging Waves and Optics 4 Two-beam interference Example: A beam from a Nd:YAG laser ( λ 0 =1064 nm) is split into two beams of equal intensity. These two beams are directed from different directions at the same point on a photographic film. What should the angular separation between the beams be if the dark fringes in the exposed film are to be 25 μm apart?
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imaging Waves and Optics 5 Two-source Interference requires coherent point sources imaging Waves and Optics 6 Young’s Double-slit Experiment pathlength difference max intensity min intensity large distances θ sin a x = λ θ m a = sin λ θ + = 2 1 sin m a a D y θ sin D y
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imaging Waves and Optics 7 Young’s Double-slit Experiment Example: Coherent light from a mercury arc lamp passes through a
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