In a single$-$slit diffraction pattern on a flat screen, the central bright fringe is $1\mathrm{.}2$ cm wide when the slit width is $3\mathrm{.}2105$ m$.$ When the slit is replaced by a second slit, the wavelength of the light and the distance to the screen remaining unchanged, the central bright fringe broadens to a width of $1\mathrm{.}9$ cm$.$ What is the width of the second slit? It may be assumed that is so small that sin $$ tan $.$