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Interference-and-Diffraction

# Interference-and-Diffraction - Wave Optics Wave Optics...

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Wave Optics

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Wave Optics Water wave passing though an opening Sharp shadow The wave nature of light is needed to explain various phenomena Interference Diffraction The particle nature of light was the basis for ray (geometric) optics
Interference of light Young’s double slit experiment Observed interference fringes

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Interference Constructive interference occurs when the path-length difference is integer multiple of the wavelength In small-angle approximation, angle of bight fringes is The position of bright fringes can be found The fringe spacing is independent of m λ θ m sin d r = = ... , 3 , 2 , 1 , 0 m , d L m y tan L y m = = = λ θ ... 3 , 2 , 1 , 0 m , d m m = = λ θ d L y y y m 1 m λ = - = +
Interference Destructive interference occurs when the path-length difference is a half-integer number of wavelengths Dark fringes are located exactly halfway between the bright fringes. ... , 2 , 1 , 0 m 2 1 m r = + = λ ... , 2 , 1 , 0 m , d L 2 1 m ' y m = + = λ

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Intensity in a double-slit interference In general, intensity proportional to the square of the amplitude of the wave. The net amplitude of superimposed wave is given by The phase difference at position y is The light intensity is then = 2 cos a 2 A φ Where a is the amplitude of each individual wave y L d 2 sin d 2 r 2 λ π λ θ π λ π φ = = = y L d cos I 4 I 2 1 double λ π
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