What is the width of the second slit in a single-slit diffraction experiment?

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In a single-slit diffraction experiment, the width of the central bright fringe changes when the slit is modified. Initially, with a slit width of 3.48E-5 m, the central fringe measures 1.37 cm. Upon replacing the slit with a second one, the fringe width increases to 1.88 cm while keeping the wavelength and screen distance constant. The problem requires determining the width of the second slit using the relationship between slit width and fringe width. The assumption is made that the angle θ is small enough for sinθ to approximate tanθ.
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Homework Statement



In a single-slit diffraction pattern on a flat screen, the central bright fringe is 1.37 cm wide when the slit width is 3.48E-5 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 1.88 cm. What is the width of the second slit? It may be assumed that θ is so small that sinθ ∼ tanθ.


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