Why does obliquity affect amplitude?

Question

In experiments like half period zone diffraction, the amplitude of waves decreases due to the obliquity of the point when we move away from the centre. What is the concept behind it?

Answer 1

Obliquity was at first a "fudge factor" added by Fresnel to Huygens' principle to make the latter fully agree with experiment, i.e. that the Huygens secondary wavelets experimentally did not propagate backwards relative to the "mean", ray-theoretic light propagation direction.

Later, Kirchhoff showed that the obliquity factor could in fact be derived by interpreting Huygens' principle as a kind of Green Function solution to the Helmholtz equation, where the Huygens secondary source is the Green function, i.e. the solution $\psi = e^{i\,k\,r}/r$ of the inhomogeneous Helmholtz equation $(\nabla^2+k^2)\,\psi(\vec{r}) = \delta(\vec{r})$, whence other solutions can be built by linear superposition. However, Kirchhoff needed to make certain, somehwhat arbitrary assumptions about the boundary conditions at the opaque screen and about the value of the scalar field at the boundary between screen and aperture to make his reasoning work. These conditions are intuitively reasonable, but there is no reason why others cannot sometimes prevail in unusual conditions

The significance of the Helmholtz equation is that it is fulfilled by all six Cartesian components of the elecrtromagnetic field ($E_j$ and $B_j$) in a homogeneous, linear medium.