The Huygens-Fresnel principle describes propagation by coherent addition of secondary-wave contributions from a wavefront or aperture. Their complex amplitudes, including relative wave phases, must be summed before calculating light intensity. The Fresnel propagator follows by retaining quadratic propagation wave phase in the paraxial approximation.
Let a plane incident wavefront first meet a flat interface at , and let another point on that front reach on the interface after . Its path has length . The secondary wavelet from has radius in the second medium; the new wavefront through is tangent to it at . Right triangles with common hypotenuse give and , where both ray angles are measured from the interface normal. Consequently , which is Snell's law. The construction uses phase velocities in homogeneous isotropic media.
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The Huygens–Fresnel principle is a fundamental concept in the field of wave optics that describes how waves propagate and interfere. Named after Dutch physicist Christiaan Huygens and later expanded by the French physicist Augustin-Jean Fresnel, the principle provides a way to analyze the propagation of wavefronts, such as light waves.
