Diffraction
Bending of Waves

The spreading out of waves as they pass through an aperture or around an obstacle.

Intensity Profile

When a plane wave passes through a narrow slit, it does not travel straight through but spreads out into the region of the geometrical shadow. This creates a diffraction pattern on a distant screen consisting of a central bright fringe flanked by alternating dark and bright fringes.

The intensity $I$ at an angle $\theta$ is governed by the slit width $a$ and the wavelength $\lambda$.

$$ I(\theta) = I_0 \left( \frac{\sin \left( \frac{\pi a \sin \theta}{\lambda} \right)}{\frac{\pi a \sin \theta}{\lambda}} \right)^2 $$
Real World Analogy

Water Waves in a Harbor

Imagine ocean waves striking a breakwater with a small gap. Instead of passing through as a straight beam of water, the waves spread out radially from the gap into the harbor. If the gap is small compared to the wavelength, the spreading is more pronounced.

Every Point is a Source

The Huygens-Fresnel principle states that every point on a wavefront acts as a source of secondary spherical wavelets. The sum of these wavelets determines the form of the advancing wave.

$$ E(P) \propto \int_{\text{slit}} \frac{e^{ikr}}{r} \, dS $$
Concept

Wavelets Interfering

When a plane wave hits a slit, we can imagine the slit as being filled with many tiny point sources. These sources emit waves that interfere with each other, causing the diffraction pattern.

The Airy Disk

When light passes through a circular aperture, such as a camera lens or a telescope, it forms a diffraction pattern known as an Airy disk. This consists of a bright central circular region surrounded by fainter concentric rings.

$$ \theta = 1.22 \frac{\lambda}{D} $$
Resolution Limit

Rayleigh Criterion

Because of the Airy disk, two closely spaced point sources (like stars) will blur together if their central maxima are too close. This limits the maximum resolving power of any optical system.

Academic References