The diffraction pattern shown is produced by passing He$-$Ne laser light $\backslash ((\backslash$lambda$=632\mathrm{.}8\backslash$mathrm$\{$~nm$\})\backslash )$ through a single slit and viewina the pattern on a screen $1\mathrm{.}84$ m behind the slit.

$($a$)$ What is the width of the slit?

$\backslash (\backslash$mu $\backslash$mathrm$\{$m$\}\backslash )$

$($b$)$ If monochromatic light with a wavelength of $500$ nm was instead used with this slit, would the distance indicated in the figure be greater than or less than $15\mathrm{.}2$ cm $?$

less than $15\mathrm{.}2$ cm $,$ since smaller wavelengths have a wider spread to their diffraction patterns