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    I'm writing a report on diffraction and a little confused on the conditions for a minimum/maximum given for single and double slit diffraction.

    I know for single slit diffraction, conditions for minima are given by \sin\theta=\frac{\lambda/2}{b/2}=\frac{n\lambda}{b}, and that the equation for maximum for double slit diffraction is given by \sin\theta=\frac{n\lambda}{d}, but aren't these the same equations? So why do they give different results i.e. maxima for one, and minima for the other?

    And for single slit diffraction, wouldn't \sin\theta=\frac{n\lambda}{b} give the conditions for maxima as well as for minima?
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    The equation normally given for the double slit case is

    y = \frac{d \lambda}{a}

    y is the fringe separation. That is, the distance between two adjacent bright or dark fringes on a screen a distance d from the sources. The sources are a distance a apart. There is no "n" in the formula.

    The single slit equation is for an angle and is usually given as

    sin \theta = \frac{n \lambda}{a}

    (or just theta if the angle is very small)

    and is the angular position of the n th minimum. The equation is derived for destructive interference where the path difference is half a wavelength. Hence the lambda / 2 in your formula.
    Here a is the width of the single slit.
    There is no "d" in the formula.
 
 
 
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