Fraunhofer diffraction of unequal slits (source code)

= Fraunhofer diffraction of unequal slits

Two equally illuminated slits of different widths have field <amplitudes> $A_j(\theta)\propto w_j\operatorname{sinc}(\pi w_j\sin\theta/\lambda)$. Their <interference> <intensity> is $A_1^2+A_2^2+2A_1A_2\cos(2\pi d\sin\theta/\lambda+\delta)$. 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.