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I had answered a question Single Slit Diffraction Experiment, telling why the central maximum is the brightest one, but it asks:

Why is the central maximum twice as wide as the others?

Now, that is tricking me, I have tried my best to search the reason and seen many diagrams, but I can't understand why.

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  • $\begingroup$ Central fringe width = distance between first minimas = $\frac{2λx}l\\$; For non-central fringes, width = distance between 2 consecutive minimas = $\frac{(n+1)λx}l - \frac{nλx}l = \frac{λx}l$ $\endgroup$
    – Shub
    Commented Nov 17, 2022 at 7:09

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You can know that from the derivation of fringe width in single slit experiment, though I will give you a simple answer, without much mathematics.

If you look at diagrams of Fraunhofer single-slit diffraction patterns, you will see that the central maximum is symmetrical about the center line. All the other maxima and minima are found on just one side of the center line. Of course, the pattern as a whole is also symmetrical about the center line.

Both the mathematics and experimental results show that the positions of the minima are at distances from the center line that depend on the details of the particular experiment.

Those minima distances are found fairly accurately by multiplying a constant (which depends on the experiment) by a whole number (that number is $1$ for the first two minima and $2$ for the second two minima, and so on). There is no minimum on the center line, of course (corresponding to the number $0$).

Let $\text{Min}_1$ be the distance from the center line to the first two minima, one on each side of the center line. Let the distance of the second two minima from the center line be $\text{Min}_2$, and so on. $\text{Min}_2$ is about twice of $\text{Min}_1$. The width of the maxima is roughly the distance between adjacent minima. So, all the secondary maxima are about $\text{Min}_1$ in width.

However, the distance between the two first two minima, on each side of the center line is $2 \times \text{Min}_1$. The central maximum lies between the first two minima (located on opposite sides of the center line). All the secondary bright fringes lie between adjacent minima on the same side of the center line. So now you can see why the width of the central maximum is about twice the width of the other bright fringes

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