 Fraunhofer diffraction of unequal slits

ID: fraunhofer-diffraction-of-unequal-slits

Two equally illuminated slits of different widths have field amplitudes

A_{j} (θ) \propto w_{j} sinc (π w_{j} sin θ / λ)

A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos (2 π d sin θ / λ + δ)

. Near the centre,

A_{2} / A_{1} = w_{2} / w_{1}

, so the local maximum-to-minimum ratio is

(w_{1} + w_{2})^{2} / (w_{2} - w_{1})^{2}

. At one slit envelope's zero the interference visibility vanishes even if the other slit still transmits.

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