An interference pattern is produced by light with a wavelength $570$ nm from a distant source incident on two identical parallel slits separated by a distance $($between centers$)$ of $0\mathrm{.}470$nm$.$ If the slits are very narrow, what would be the angular position of the first$-$order, two$-$slit, interference maxima? What would be the angular position of the second$-$order, two$-$slit, interference maxima in this case? Let the slits have a width $0\mathrm{.}280$nm$.$ In terms of the intensity I$0$ at the center of the central maximum, what is the intensity at the angular position of sigma$1?$ What is the intensity at the angular position of sigma$2?$