Fraunhofer diffraction

Fraunhofer diffraction

1. What Fraunhofer Is (far-field)

Fraunhofer diffraction = diffraction where incident light is collimated (plane wave) and pattern observed at focal plane of a lens (or at infinity) — so rays are parallel and phase is linear in aperture coordinate. Mathematically, pattern is Fourier transform of aperture:

Achieved by placing source at focus of collimating lens and screen at focus of converging lens; wavefronts are plane, calculations simple.

2. Conditions vs Fresnel

Feature	Fresnel (near-field)	Fraunhofer (far-field)
Distances	finite	effectively infinite (lenses)
Wavefronts	spherical	plane
Maths	Fresnel integrals / zones	sinc / Bessel / Fourier
Setup	no lenses needed	two lenses (collimate + focus)

Fraunhofer is the far-field limit of Fresnel as distance $D ≫ a²/λ$.

3. Patterns Covered Next

• Single slit:

,

• Double slit: interference × single-slit envelope:

,

• Circular aperture: Airy disc

, $q=(2π a sinθ)/λ$, first dark $sinθ≈1.22λ/(2a)$.

• Grating: many slits — sharp maxima.

4. Central Uses

Fraunhofer patterns are how lenses, telescopes, spectrometers work — their resolution limits are diffraction based.

5. Worked Setup

Lens L1 collimates point source S at its focus → plane wave hits slit/aperture → lens L2 focuses diffracted rays → pattern at its focal plane, position y = f·tanθ ≈ f·θ for small θ ✓
Without lenses, move screen far away D≫a²/λ to approximate Fraunhofer.

6. Exam Points

• Define Fraunhofer with ray diagram (two lenses) — 5 marks, very frequent.
• Condition $D≫a²/λ$ and difference vs Fresnel (table) — 5 marks, very frequent.
• Mention pattern is Fourier transform — 3 marks.