Learning Objectives
- Understand Huygens' principle and its applications
- Study Young's double slit experiment and interference
- Learn about diffraction at a single slit
- Understand polarisation and its applications
- Differentiate between interference and diffraction
Key Concepts
Huygens' Principle
Each point on a wavefront acts as a source of secondary wavelets. The new wavefront is the envelope of all secondary wavelets.
Used to explain reflection and refraction of light. Proves that light slows down in a denser medium (wave theory).
Coherent Sources
Sources that emit light with a constant phase difference. Required for sustained interference.
Methods of obtaining coherent sources: division of wavefront (YDSE), division of amplitude (thin film).
Young's Double Slit Experiment (YDSE)
Path difference: Δ = d sin θ ≈ dy/D (for small angles), where d = slit separation, D = screen distance.
Bright fringe (constructive): Δ = nλ → y_n = nλD/d (n = 0, 1, 2, ...)
Dark fringe (destructive): Δ = (2n-1)λ/2 → y_n = (2n-1)λD/(2d)
Fringe width: β = λD/d (spacing between consecutive bright or dark fringes).
Intensity: I = 4I₀ cos²(φ/2), where φ = 2πΔ/λ is the phase difference.
At maxima: I_max = 4I₀. At minima: I_min = 0 (for equal intensity sources).
If intensities are unequal: I_max = (√I₁ + √I₂)², I_min = (√I₁ - √I₂)².
Diffraction
Bending of light around obstacles or through narrow openings (comparable to wavelength).
Single slit diffraction:
Minima at: a sin θ = nλ (n = 1, 2, 3, ...)
Central maximum: angular width = 2λ/a. Linear width = 2λD/a.
Secondary maxima at: a sin θ ≈ (2n+1)λ/2
Central maximum is twice as wide as secondary maxima and much more intense.
Polarisation
Restriction of electric field vibrations to a single plane. Only transverse waves can be polarised.
Malus's Law: I = I₀ cos²θ (intensity through analyser at angle θ to polariser).
Brewster's Law: tan θ_B = n₂/n₁ (reflected light is completely polarised at Brewster's angle).
At Brewster's angle: reflected and refracted rays are perpendicular (θ_B + θ_r = 90°).
Polarisation methods: reflection, double refraction, selective absorption (Polaroid), scattering.
Resolving Power
Microscope: R.P. = 2n sin θ / λ (n sin θ = numerical aperture).
Telescope: R.P. = D/1.22λ = a/1.22λ (D = aperture diameter).
Summary
Wave optics explains phenomena that ray optics cannot: interference, diffraction, and polarisation. Huygens' principle describes wavefront propagation. Young's experiment demonstrates interference with fringe width β = λD/d. Single slit diffraction shows a central maximum with side fringes. Polarisation proves the transverse nature of light and follows Malus's law and Brewster's law.
Important Terms
- Interference: Superposition of two coherent waves producing maxima and minima
- Diffraction: Bending of light around obstacles
- Coherent Sources: Sources with constant phase difference
- Fringe Width: Spacing between consecutive bright/dark fringes, β = λD/d
- Polarisation: Confinement of vibrations to one plane
- Brewster's Angle: Angle of incidence for complete polarisation of reflected light
Quick Revision
- YDSE: bright at dy/D = nλ; dark at dy/D = (2n-1)λ/2; β = λD/d
- Single slit: minima at a sin θ = nλ; central max width = 2λD/a
- Malus's law: I = I₀ cos²θ
- Brewster's law: tan θ_B = n; reflected and refracted rays at 90°
- Interference: redistribution of energy; Diffraction: bending around obstacles
- R.P. of telescope = D/(1.22λ)