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What is single slit diffraction?
The simplest diffraction pattern to analyze is that produced by a long, narrow slit. In this section we discuss the locations of the minima and maxima in the patter. Figure below show a plan wave falling at normal incidence on a slit of width a . let us first consider the central point P0. Rays that leave the slit parallel to the central horizontal axis are brought to a focus at P0. These rays are certainly in phase at the plane of the slit, and they remain in phase as they are brought to a focus by the lens. Since all rays arriving at P0 are in phase, they interfere constructively and
produce a maximum of intensity at P0.
We now consider another point on the screen. Light rays that reach P1 in figure below leve the slit at the angle θ, as shown. The ray xP1 passes undeflected through the center of the lens and therefore determines θ Ray r1 originates at the top of the slit and ray r2 at its centre. If θ is chosen so that the distance bb in the figure is one half wavelength, r1 and r2 are out of phase and interfere destructively at p1. The same is true for a ray just below r1 and another just be r2. In fact for every ray passing through the upper half of the slit, there is a corresponding ray passing through the lower half, originating at a point a/2 below the first ray, such that the two ray are out of phase at p1. Every ray arriving at p1 from the upper half of the slit interferes destructively with one coming from the bottom half of the slit. The intensity at p1 is therefore zero, and p1 is the first minimum of the diffraction pattern.
Since the distance bb’ equals (a/2) sin θ, the condition for the first minimum can be written as a/2sin θ = λ/2 or a sin θ = λ.
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