Derive an expression for the intensity of the diffraction pattern obtained due to Fraunhofer diffraction from a single slit.

Fraunhofer diffraction occurs when light waves diffract after passing through a narrow aperture or slit, resulting in a pattern of bright and dark fringes. When a beam of light passes through a single slit, it spreads out due to diffraction, creating an interference pattern. To derive an expression for the intensity of the diffraction pattern resulting from a single slit, we can use Huygens' principle and consider the contributions of different portions of the slit to the overall diffraction pattern.

Let's consider a coherent light source emitting a plane wavefront incident on a single slit of width \(a\). According to Huygens' principle, each point on the slit can be treated as a secondary source of spherical waves. The phase difference between waves emanating from __________ _________ _________ ___ ______ __________ ____ _______.
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