Light Wave Interference — Double-Slit, Thin Films & Michelson Interferometer Explained | Chapter 35 of University Physics

Chapter 35 explores the wave nature of light through interference phenomena, from Young’s double-slit experiment to thin-film color effects and the precision of the Michelson interferometer. Understanding these patterns is crucial for applications in spectroscopy, metrology, and optical engineering.

Watch the full video summary on YouTube to see visual demonstrations of each interference pattern.

Principles of Interference & Coherent Sources

Interference arises when two or more light waves overlap, with superposition leading to bright and dark fringes. Coherent sources maintain a constant phase relationship and identical frequency, making stable interference patterns possible—lasers are the most common coherent sources in the lab.

Young’s Two-Slit Experiment

In Young’s classic setup, light from a single source illuminates two narrow slits separated by distance d. Bright fringes (constructive interference) occur at angles satisfying:

d sin θ = m λ (m = 0, ±1, ±2…), while dark fringes (destructive) follow d sin θ = (m + ½) λ. On a screen at distance R, the fringe position is yₘ = R m λ / d.

Intensity Distribution

The combined electric field amplitude is E = 2E₀ cos(Δφ/2), giving intensity:

I = I₀ cos²(Δφ/2), where the phase difference Δφ = (2π/λ) (path difference). These formulas quantify fringe contrast and spacing in precision measurements.

Thin-Film Interference

Thin films—like soap bubbles or anti-reflective coatings—produce colorful patterns from reflections at their two surfaces. Constructive reflection (no phase shift) occurs when:

2 n t = m λ, and destructive when 2 n t = (m + ½) λ, where t is film thickness and n its refractive index. Phase shifts on reflection can reverse these conditions.

Michelson Interferometer

The Michelson interferometer splits light into two paths with a beam splitter and recombines them to form interference fringes. Moving one mirror by distance Δx changes the optical path by 2 Δx, shifting m fringes and yielding wavelength: λ = 2 Δx / m. This setup underlies precision length measurements and was key in disproving the luminiferous ether.

Conclusion

Interference patterns reveal the fundamental wave nature of light and enable high-resolution optical techniques—from measuring slit widths and atomic spacings to creating holograms. Mastering these phenomena opens the door to advanced applications in spectroscopy, fiber optics, and quantum optics.

If you found this breakdown helpful, be sure to subscribe to Last Minute Lecture for more chapter-by-chapter textbook summaries and academic study guides.