Theme C · Wave Behaviour · SL 5h + HL extension 6h

C.3 Wave Phenomena

What happens when waves meet boundaries, apertures, or each other?

When a wave encounters a boundary between two media, it can be reflected, transmitted, or both — and refraction (the change in direction as speed changes) governs the transmitted part. Snell's law precisely relates the angles and refractive indices; total internal reflection occurs when the angle of incidence exceeds the critical angle, which is the basis of optical fibres.

Superposition is the other great principle: when two waves occupy the same space, the displacements add algebraically. Constructive interference (path difference = nλ) produces bright fringes; destructive interference (path difference = (n + ½)λ) produces dark ones. Young's double-slit experiment demonstrated that light is a wave — the bright and dark fringes are direct evidence of wave interference.

Young's double-slit experiment uses light of wavelength 600 nm, with slits separated by 0.25 mm. The screen is 1.5 m from the slits. Calculate the fringe separation. What would happen to the fringes if you used blue light instead of red?

Key equations

Snell's law: n₁/n₂ = sinθ₂/sinθ₁ = v₂/v₁

Critical angle: sin(θ_c) = n₂/n₁ (for n₂ < n₁)

Constructive interference: path difference = nλ

Destructive interference: path difference = (n + ½)λ

Young's double slit: s = λD/d

HL Single-slit first minimum: θ = λ/b

HL Diffraction grating: nλ = d sinθ

What students must understand

Wavefronts and rays as representations of wave propagation in 2D and 3D
Wave behaviour at boundaries: reflection, refraction, transmission
Wave diffraction around bodies and through apertures — qualitative
Snell's law and refractive index; critical angle and total internal reflection
Superposition: algebraic addition of displacements when waves coincide
Coherence required for stable interference patterns
Constructive and destructive interference conditions in terms of path difference
Young's double-slit: s = λD/d; fringe separation increases with wavelength, decreases with slit separation
HL Single-slit diffraction: intensity pattern, first minimum at θ = λ/b
HL Single-slit pattern modulates the double-slit interference pattern
HL Diffraction gratings: nλ = d sinθ; sharp maxima for each order

Linking questions

What does Young's double-slit experiment reveal about the nature of light? → E.2 Quantum Physics
What evidence shows that particles have wave-like properties? → E.2 Quantum Physics (NOS)