Answer some questions about the mathematics of multiple-slit diffraction, for 10 points each.
[10e] This phenomenon occurs precisely when “d sine theta” is an integer multiple of the wavelength. In this phenomenon, two waves in superposition add to create one with larger amplitude.
ANSWER: constructive interference [prompt on interference]
[10h] This exact, doubly-eponymous diffraction integral can be applied to multiple-slit interference by treating the entire grating as the aperture. The Fresnel and Fraunhofer approximations simplify this integral in the near- and far-field, respectively.
ANSWER: Rayleigh–Sommerfeld diffraction integral [do not accept or prompt on partial answer]
[10m] The intensity profile of the multiple-slit far-field pattern still follows the envelope given by this function squared, which has one large central peak. This function is important in signal processing because it is the Fourier transform of a rectangular pulse.
ANSWER: sinc [or cardinal sine; accept sin x over x, with any symbol for x; accept sin pi x over pi x; reject “sin” or “sine” or “inverse sin” or “arcsin”]
<S, Physics>