Derive the expression for shape factor for radiation emitting from a surface ‘i’ and reaching the surface ‘j’.

The shape factor, denoted by \( F_{ij} \), represents the fraction of radiation leaving surface \( i \) that reaches surface \( j \). It is essential in radiative heat transfer analysis, helping determine the exchange of radiant energy between surfaces. The expression for the shape factor depends on the geometry of the surfaces and their relative positions.

Let's consider two arbitrary surfaces \( i \) and \( j \) with areas \( A_i \) and \( A_j \), respectively. The shape factor ______ _____ _____ _____ _______ _________ _______ _____ ____.
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