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

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SUMMARY

The width of the central diffraction maximum in a single slit experiment can be calculated using the formula d/2 = Dλ/b, where d is the width of the central maximum, D is the distance from the slit to the screen, λ is the wavelength of the light, and b is the width of the slit. This relationship arises from the principles of Fraunhofer diffraction, specifically the interference pattern created by light passing through a narrow aperture. Understanding this formula is essential for accurately predicting diffraction patterns in optics.

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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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