IGNOU MPH 13 2026 - Using the scalar theory of diffraction, obtain the expression fo

Question

Using the scalar theory of diffraction, obtain the expression for Fresnel diffraction integral.

19 Jan 2026

Answer :

Word Count : 332

The scalar theory of diffraction assumes that the electromagnetic field can be represented by a scalar function (U(\mathbf{r}, t)) that satisfies the Helmholtz equation: [ \nabla^2 U + k^2 U = 0 ] where (k = \frac{2\pi}{\lambda}) is the wave number. Consider a monochromatic wave incident on an aperture in the plane (z = 0), and let (U_0(x_0, y_0)) denote the field distribution in this plane. We want the field (U(P)) at a point (P(x, y, z)) in space beyond the aperture. According to Huygens-Fresnel principle, each point on the aperture acts as a secondary source emitting spherical wavelets. The contribution from an element (dS_0 = dx_0 dy_0) at ((x_0, y_0, 0)) to the point (P)

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