Huygens' Principle and Diffraction

In the 1600s, Christiaan Huygens proposed a revolutionary way to think about wave motion. He suggested that a wavefront isn't just a single moving line, but a collection of infinite points. According to Huygens' Principle, every point on a wavefront acts as a source of tiny, spherical secondary wavelets that spread out in the forward direction at the same speed as the wave itself. The new wavefront at any later time is the tangent surface that touches all these individual wavelets. This explains why waves don't just disappear; they are constantly 'rebuilding' themselves as they travel through a medium.

When a wave encounters an obstacle or a small opening (a slit), it doesn't just stop or pass through cleanly. It bends. This phenomenon is called diffraction. Using Huygens' Principle, we can see why: when a wave hits a barrier with a slit, only the wavelets located inside the slit can pass through. Because there are no wavelets next to them to 'cancel' their sideways expansion through interference, these edge wavelets spread out into the 'shadow' region behind the barrier. This causes the wave to fan out, filling the space behind the opening.

The reason we notice sound diffracting but not light comes down to the diffraction condition: $\lambda \approx a$. For significant diffraction to occur, the wavelength $\lambda$ must be comparable to the size of the opening $a$.

- Sound waves have wavelengths ranging from roughly $1.7\text{ cm}$ to $17\text{ m}$. Since doorways and hallways are about $1-2\text{ m}$ wide, sound waves 'fit' the criteria for massive diffraction. - Visible light has tiny wavelengths, between $400\text{ nm}$ and $700\text{ nm}$ ($0.0000004\text{ m}$). A standard doorway is millions of times wider than a light wave, so light passes through with negligible bending, creating sharp shadows.