devaultc
Nov13-10, 06:50 PM
1. The problem statement, all variables and given/known data
Consider a Fraunhofer diffraction pattern due to two unequal slits. Let a and b be the unequal slit widths and c the distance between their centers. Derive an expression for the intensity of the pattern for and diffraction angle \theta, assuming the arrangement to be illuminated by perpendicular light of wavelength \lambda.
2. Relevant equations
Fresnel-Kirchoff formula: Up = C\int E^(ikr)dA
E(kz) = FT{A(z)} where A(z) is the aperture function and FT is Fourier Trnasform
3. The attempt at a solution
My attempt has been to express the double slit as an aperture function A(z) as the sum of the rectangle function rect|(z+c)/a| + rect|(z-c)/b| and take the FT of A(z). I know the general FT of a rectangle function is sinc() but I am not sure how to show that and if I do, how do I interpret my results? Thanks
Consider a Fraunhofer diffraction pattern due to two unequal slits. Let a and b be the unequal slit widths and c the distance between their centers. Derive an expression for the intensity of the pattern for and diffraction angle \theta, assuming the arrangement to be illuminated by perpendicular light of wavelength \lambda.
2. Relevant equations
Fresnel-Kirchoff formula: Up = C\int E^(ikr)dA
E(kz) = FT{A(z)} where A(z) is the aperture function and FT is Fourier Trnasform
3. The attempt at a solution
My attempt has been to express the double slit as an aperture function A(z) as the sum of the rectangle function rect|(z+c)/a| + rect|(z-c)/b| and take the FT of A(z). I know the general FT of a rectangle function is sinc() but I am not sure how to show that and if I do, how do I interpret my results? Thanks