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Huygens' principle and its applications

Wavefronts and Huygens' principle · Physics

Transverse wave

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A travelling wave ribbon. Raise the amplitude to make it taller, the frequency to make it faster.

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Study notes

Use Huygens' construction to answer: (a) A plane wavefront hits a small obstacle of size ~λ. What happens behind it? (b) A plane wavefront in air meets glass at an angle; which part of the refracted envelope forms first? (c) Why is there no backward-propagating wavefront? Step 1: Wavelets from the unblocked parts spread into the geometric shadow (hemispherical wavelets have no "shadow" of their own). The envelope behind the obstacle is a nearly complete wavefront with slight ripples — diffraction: light bends around obstacles of wavelength size. Ray optics would predict a sharp shadow. Step 2: Wavelets excited first (where the wavefront touches glass first) have been expanding in slow glass longer, so they are smaller; wavelets excited later are bigger. The envelope joining them tilts toward the normal — refraction, derived in the next topic with the exact Snell's-law geometry. Step 3: Strictly, each wavelet is a full sphere including a backward part; the backward envelope would be a regressing wavefront. It is not observed, so Huygens (and Fresnel's obliquity factor, which weights forward emission) simply discard it — an empirical rule that works, later justified by full wave theory.

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