$6.[15$ pts$.]$ A beam of $\backslash (633\backslash$times $10^\{-9\}\backslash$mathrm$\{$~m$\}\backslash )$ light shines on two slits that are separated by a distance of $\backslash (3\mathrm{.}0\backslash$times $10^\{-4\}\backslash$mathrm$\{$~m$\}\backslash ).$ Each slit has a width of $\backslash (4\mathrm{.}5\backslash$times $10^\{-6\}\backslash$mathrm$\{$~m$\}\backslash ).$ An interference pattern appears on a screen that $1\mathrm{.}67$ m away from the slits. Assume everything is done in air.

$($A$).$ What is fringe angle of the second minimum for the single$-$slit interference pattern?

$($B$).$ How far from the center of the central bright spot does the second single$-$slit minimum occur?

$($C$).$ A double$-$slit interference pattern will overlap with the single$-$slit pattern What is the order number of the double$-$slit maximum that would occur at approximately the same location as the second order single$-$slit interference minimum found in part B$?$

$($D$).$ If you placed the slits and screen under water $\backslash (($n$=1\mathrm{.}33)\backslash ),$ would your answer to part B increase, decrease, or stay the same? Explain your answer.