Diffraction

Diffraction

1. What Diffraction Is (vs Interference)

Diffraction = bending of light around edges/obstacles and spreading into geometrical shadow, due to interference of many coherent secondary wavelets from different parts of the same wavefront (Huygens–Fresnel principle).

• Interference: superposition of two separate beams (few sources) → equally spaced fringes with all maxima equal intensity.
• Diffraction: superposition of continuous secondary sources across one aperture → envelope with decreasing maxima, central brightest, with minima at different angles; fringe width not equal, intensities fall off.

Both are interference at heart, but diffraction is interference within one wavefront.

2. Huygens–Fresnel Principle

Every point on a wavefront acts as a secondary source; disturbance at $P$ is sum of secondary wavelets:

Phase depends on path length; amplitude ~ aperture function.

3. Two Types

• Fresnel diffraction: source and screen at finite distances, wavefronts spherical, no lenses; maths harder (Fresnel zones).
• Fraunhofer diffraction: source and screen at effective infinity (plane waves, lens focuses) → far-field, easier Fourier-type: pattern is Fourier transform of aperture.

Next topics focus on Fraunhofer.

4. Why Shadows Not Sharp

If wavelength $λ ≪$ aperture $a$, diffraction spread $θ ≈ λ/a$ tiny ⇒ shadow sharp (geometric optics limit). If $λ∼a$, spread large ⇒ noticeable bending (this is why sound diffracts around doors but light not around buildings).

5. Worked Intuition

A 0.1 mm slit with λ=600 nm: first minima at θ≈ λ/a =6 mrad (≈0.34°) — measurable spread.

A hair vs radio wave: λ hair? Optical λ ~500 nm vs hair  50 µm: a≫λ ⇒ small diffraction; radio λ ~1 m vs building 10 m: a≈λ ⇒ strong diffraction around building.

6. Exam Points

• Define diffraction and distinguish from interference — 5 marks, very frequent (table comparison).
• State Huygens–Fresnel principle — 3-5 marks, frequent.
• Fresnel vs Fraunhofer with diagram (lenses vs not) — 5 marks, very frequent.
• Explain why geometrical shadow not perfectly sharp — 3 marks.