Overview
This lecture covers the principle of superposition in waves, including constructive and destructive interference, phase and path difference, and applications such as Young's double-slit experiment and diffraction gratings.
Superposition Principle
- Superposition occurs when two or more waves meet and combine at a point.
- The resultant displacement at any point is the sum of the individual wave displacements there.
- Supercrest forms when crests combine; supertrough when troughs combine; crest and trough cancel.
Interference Types
- Constructive interference: waves in phase reinforce to form larger amplitude.
- Destructive interference: waves in antiphase cancel, resulting in zero amplitude.
- Sound waves, water waves, microwaves, and light can all demonstrate interference.
Phase and Path Difference
- Phase difference measures how far one point/wave is from another in the wave cycle, in radians or degrees.
- In phase: phase difference is 0 or multiples of 360°; out of phase: odd multiples of 180°.
- Path difference is the extra distance one wave travels compared to another.
- Constructive interference: path difference = nλ; destructive: path difference = (n + ½)λ.
Wave Interference Examples
- Ripple tanks show constructive interference (crests/troughs meet) and destructive interference (crest meets trough).
- Microwaves and sound waves also produce alternating loud (constructive) and quiet (destructive) areas due to interference.
Young’s Double-Slit Experiment
- Demonstrates light interference and evidence for wave nature of light.
- Monochromatic light through two slits creates a pattern of bright (constructive) and dark (destructive) fringes.
- Constructive: path difference = nλ; destructive: path difference = (n + ½)λ.
- Formula for fringe width: λ = ax/D (λ=wavelength, a=slit separation, x=fringe width, D=distance to screen).
Coherence
- Coherent sources have a constant phase difference and same frequency.
- Stable interference patterns require coherent and similar-amplitude sources.
Diffraction Grating
- A plate with many equally spaced slits produces sharper, more widely spaced bright fringes than double slits.
- Diffraction grating equation: nλ = d sinθ (n=order, λ=wavelength, d=slit spacing, θ=angle).
- Grating spacing d = 1/(lines per mm).
White Light and Spectra
- White light produces a spectrum through a grating due to different wavelengths diffracting by different amounts.
- Zero-order maximum remains white; higher orders show colour separation (spectra).
Applications of Diffraction Grating
- Used in X-ray crystallography, spectrometers, lasers, optical devices, and in everyday items like CDs.
Key Terms & Definitions
- Superposition — The combination of wave displacements at a point.
- Constructive Interference — In phase waves reinforce each other, increasing amplitude.
- Destructive Interference — Antiphase waves cancel each other, reducing amplitude.
- Phase Difference — The fraction of a wave cycle separating two points, measured in radians or degrees.
- Path Difference — Extra distance one wave travels compared to another.
- Coherent Sources — Sources with constant phase difference and same frequency.
- Diffraction Grating — Device with multiple slits, producing sharp interference patterns.
Action Items / Next Steps
- Review the 10.3.2 Superposition worked examples pack for exam-style questions.
- Ensure familiarity with key formulas and when to apply them.