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Unformatted text preview: imaging Waves and Optics 1 Interference • twobeam interference • Young’s experiment • Michelson interferometer • thin film interference • FabryPerot 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 r r r r r r ( ) 2 / cos 4 2 δ I I = ( ) 1 2 1 2 δ δ δ − + ⋅ − = r k k r r r 4 2 I I m = ⇒ = π δ ( ) 1 2 = ⇒ + = I m π δ imaging Waves and Optics 3 Twobeam 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 Twobeam interference • Example: A beam from a Nd:YAG laser ( λ =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? imaging Waves and Optics 5 Twosource Interference • requires coherent point sources imaging Waves and Optics 6 Young’s Doubleslit 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 imaging Waves and Optics 7 Young’s Doubleslit Experiment...
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This note was uploaded on 08/26/2008 for the course PHYSICS 603 taught by Professor Sage during the Summer '06 term at Northwestern.
 Summer '06
 sage
 Waves And Optics

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