**What is diffraction ?**

Diffraction is generally defined as the bending of light around corners such that it spreads out and illuminates areas where a shadow is expected. In general it is hard to separate diffraction from interference since both occur simultaneously.

In this experiment, we can observe the bending phenomenon of light or diffraction that causes light from a coherent source interfere with itself and produce a distinctive pattern on the screen called the diffraction pattern. Diffraction is observable when the sources are small enough that they are relatively the size of the wavelength of light. You can see this effect in the diagram below. For large slits the spreading out is small and generally unnoticeable.

For a single slit experiment we shall assume the slit width a << D. D is the separation between slit and source.

We shall identify the angular position of any point on screen by \(ϑ\)

The path difference is exhibited by the top two rays shown is

Remember that this is an approximation valid only if \(D\)

We can consider any number of ray pairings that start from a distance \(\frac{a}{2}\)

For a dark fringe, the path difference must cause destructive interference; the path difference must be out of phase by \(\frac{λ}{2}\)

For the first fringe,

For a ray emanating from any point in the slit there exists another ray at a distance \(\frac{a}{2}\)

Thus, at \(θ\)

For the next fringe, we can divide the, the slit into 4 equal parts of a/4 and apply the same logic. Thus, for the second minima

Similarly for the \(n^{th}\)

**The central maximum**

The maxima lie between the minima and the width of the central maximum is simply the distance between the 1st order minima from the centre of the screen on both sides of the centre.

The position of the minima given by \(y\)

For small \(ϑ\)

The width of the central maximum is simply twice this value

*width of central maximum*,= \(2 \frac{λD}{a}\)

*angular width of central maximum*= \(2θ\)

The diffraction pattern and intensity graph is shown below.

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