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eq_sheet2_08_1 - Equation Sheet 2 Ch 36 Single Slit(width a...

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( ) n 1 2 Ch 35 Wavelength and index of refraction: Double slit experiment: for 0 1 2 (maxima-bright fringes) for 0 1 2 (minima-dark fringes) Intensity in two-slit interfere n d sin m , m , , d sin m , m , , λ λ θ λ θ λ = = = = + = ( ) ( ) 2 1 0 2 1 2 2 2 nce: 2 4 where Thin-film interference 2 , for 0 1 2 (maxima-bright film in air) 2 , for 0 1 2 (minima-dark film in air) d I I cos , sin L m m , , n L m m , , n π φ φ θ λ λ λ = = = + = = = Equation Sheet 2 θ d P ( ) 2 m m Ch. 36 Single Slit (width ): where 1 2 3 (minima) Diffraction pattern intensity , where is the intensity at the center of the pattern Circular-aperture diffrac a a sin m m , , sin a I I sin I θ λ α π θ α θ α λ = = = = ( ) ( ) ( ) R 2 2 tion (diameter ): 1 22 Rayleigh's criterion: 1 22 Double-slits diffraction where (double slit) and same as for single slit diffraction Diffraction gratings m d sin . d . d sin I I cos d sin λ θ λ θ α θ β α π β θ α λ = = = = hw avg (N multiple slits): for 0 1 2 (maxima) half widths given by: (half-widths) angular disperion: = resolving power: X-ray diffraction: 2 for 1 d sin m , m , , , Nd cos m D d cos R Nm d sin m , m θ λ λ θ θ θ λ θ λ λ θ λ = = Δ = Δ = Δ = = Δ = = 2 3 (Bragg's law)
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