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Understanding Fraunhofer Diffraction

🌈 Wavelength Effect

Longer wavelengths (red light, ~700nm) produce wider diffraction patterns, while shorter wavelengths (violet, ~400nm) create narrower patterns. The minima positions shift proportionally with λ.

Slit Width (b)

Narrower slits cause more spreading of light. When slit width b ≈ λ, diffraction is maximum. For b >> λ, the pattern approaches geometric optics with minimal spreading.

Central Maximum

The central bright fringe is twice as wide as secondary maxima and contains ~84% of total transmitted light energy. Secondary maxima decrease rapidly in intensity.

📐 Condition for Minima (Dark Fringes)

Dark fringes occur when: b sin θ = nλ (n = ±1, ±2, ±3...)

Path difference equals integral multiple of wavelength causing destructive interference.

✨ Condition for Maxima (Bright Fringes)

Bright fringes occur approximately when: b sin θ ≈ (n+½)λ

Secondary maxima are not exactly at half-integer values due to interference envelope.

Fraunhofer Diffraction occurs when parallel light (plane waves) passes through an aperture and the diffraction pattern is observed at infinite distance (or focal plane of a lens).

Single Slit

For a slit of width b, the intensity I at angle θ is:

I(θ) = I₀
[

sin(β)


β

]²

Where β = (πb sin θ)/λ.

Minima occur at: b sin θ = nλ (n = ±1, ±2...)

Circular Aperture

For a circular hole of diameter D, the intensity is:

I(θ) = I₀
[

2J₁(x)


x

]²

Where x = (πD sin θ)/λ and J₁ is the Bessel function of first kind.

First Minimum (Airy Disk edge): sin θ ≈ 1.22 λ/D

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