How can I find the width of the central diffraction maximum.

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To find the width of the central diffraction maximum, the formula d/2 = Dλ/b is used, where d is the width of the central maximum, b is the slit width, λ is the wavelength of light, and D is the distance from the slit to the screen. This equation derives from the principles of Fraunhofer diffraction, which describes how light behaves when passing through a single slit. The central maximum width is determined by the interference pattern created by the light waves emanating from the edges of the slit. Understanding this formula requires knowledge of wave optics and the relationship between the slit dimensions and the resulting diffraction pattern. Mastery of these concepts is essential for accurately calculating the width of the central maximum.
MattDutra123
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If I am given the width of the slit (b), wavelength of the light (λ), and the distance of the slit from the screen (D), how can I find the width of the central maximum (d)? My book says d/2=Dλ/b, but with no explanation and I don't understand why. Where does this formula come from?
Thank you for your help.
 
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