Optical Diffraction & Interference Patterns Explained | Chapter 36 of University Physics

Chapter 36 delves into diffraction—the bending and spreading of light waves—and the interference patterns that arise when waves overlap. From single-slit fringes to holography, these phenomena reveal the wave nature of light and underpin technologies like spectroscopy and microscopy.

Watch the full video summary here for animated demonstrations of diffraction and interference.

Fresnel vs. Fraunhofer Diffraction

Diffraction can be classified by distance:

• Fresnel (near-field): wavefronts are curved; pattern depends on source-screen geometry.
• Fraunhofer (far-field): wavefronts are effectively planar; patterns are simpler to analyze via Fourier optics.

Single-Slit Diffraction

Light passing through a slit of width a produces a central bright fringe flanked by dimmer side fringes. The minima occur at angles satisfying:

a sin θ = m λ, where m = ±1, ±2, …. The intensity distribution is:

I(θ) = I₀ [sin(β)/β]², with β = (π a sin θ)/λ.

Multiple-Slit & Grating Interference

For N equally spaced slits (spacing d), principal maxima satisfy:

d sin θ = m λ. A diffraction grating with thousands of slits yields extremely sharp maxima and disperses white light into spectra. Its resolving power is:

R = λ/Δλ = N m, where m is the diffraction order.

X-Ray Diffraction & Bragg’s Law

X-rays diffract from crystal planes separated by distance d. Bragg’s Law gives constructive interference:

2 d sin θ = m λ. X-ray diffraction reveals atomic structures in materials.

Circular Apertures & Resolving Power

A circular aperture produces an Airy pattern—a central disk with concentric rings. The first dark ring occurs at:

sin θ ≈ 1.22 λ/D, where D is aperture diameter. The Rayleigh criterion for resolution states that two point sources are just resolved when their Airy disks overlap at this angle.

Holography

Holography records both amplitude and phase of light by interfering an object beam with a reference beam using coherent light (lasers). When illuminated:

• Virtual image appears behind the hologram.
• Real image forms in front.

Applications include 3D displays, data storage, and security holograms.

Conclusion

Diffraction and interference patterns unveil light’s wave nature and enable precise measurements—from measuring slit widths and atomic spacings to creating high-resolution imaging systems and holograms. Master these concepts to understand and design advanced optical instruments.

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