$($a$)$ Young's double$-$slit experiment is performed with $\backslash (540-\backslash$mathrm$\{$nm$\}\backslash )$ light and a distance of $2\mathrm{.}00$ m between the slits and the screen. The tenth interference minimum is observed $7\mathrm{.}95$ mm from the central maximum. Determine the spacing of the slits $($in mm $).$

$1\mathrm{.}29$

$\backslash (\backslash$checkmark $\backslash$mathrm$\{$mm$\}\backslash )$

$($b$)$ What If$?$ What are the smallest and largest wavelengths of visible light that will also produce interference minima at this location? $($Give your answers, in nm$,$ to at least three significant figures. Assume the visible light spectrum ranges from $400$ nm to $700$ nm $.)$

smallest wavelength

$\backslash (\backslash$frac$\{\backslash$sqrt$\{6\}\}\{75\}\backslash )$

$\backslash (\backslash$times $\backslash$mathrm$\{$nm$\}\backslash )$

largest wavelength

$\backslash (\backslash$times $\backslash$mathrm$\{$nm$\}\backslash )$

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