A physicist illuminates a $0\mathrm{.}63$ mm $-$wide slit with light characterized by $=532nm,$ and this results in a diffraction pattern forming upon a screen located $130$ cm from the slit assembly. Compute the width of the first and second maxima $($or bright fringes$)$ on one side of the central peak. $($Enter your answer in mm $.)$

$w_1=$

Other than the central maximum, the width of any low$-$order bright fringe will be equal to the distance between adjacent dark fringes. Use the formula for the position of a dark fringe in a single$-$slit diffraction pattern. Apply it to adjacent fringes on the same side of the central peak $($that is$,|m|=1,$ with both $m$ values positive or both negative$).$ Take care with units. mm $(1^{st}$ maxima$)$