Past exam of the physics 2 paper of the University of Oxford / 2021 / 9 / a

Let each slit alone give local light intensity $I_s$, and assume equal coherent illumination. In Fraunhofer diffraction, the two wave amplitudes differ in wave phase by $\delta =2\pi s\sin \theta /\lambda$. Adding the wave amplitudes before squaring givesFor a flat screen, $\sin \theta =x/\sqrt{d^2+x^2}$. In the paraxial region $|x|\ll d$, the double-slit interference profile is thereforeThe given $d\gg s^2/\lambda$ justifies the far-field expansion. Slit widths have been neglected; a finite width multiplies this profile by the single-slit diffraction envelope. At large angles the one-slit light intensity and geometric spreading must also be retained, rather than treating $I_s$ as constant.