Wave Optics
What is examined
Wave Optics tests Huygens' principle, interference in Young's double-slit experiment, fringe width, diffraction at a single slit, polarisation and Brewster's law.
Core rules
- Huygens: every point on a wavefront is a secondary source; the envelope gives the new wavefront. This explains reflection and refraction.
- Young's experiment: path difference at a point is xd/D. Bright fringes: d sin θ = nλ; dark: d sin θ = (n + ½)λ.
- Fringe width β = λD/d, the same for all orders. In a medium β falls because λ falls (λ' = λ/n).
- Single-slit diffraction: minima at a sin θ = nλ (n = 1, 2, ...); central maximum width 2λD/a, twice the width of the secondary maxima.
- Interference fringes are of equal width; diffraction has a broad central maximum with rapidly fading side bands.
- Polarisation shows the transverse nature of light. Brewster: tan i_p = n; reflected and refracted rays are perpendicular at i_p. Malus: I = I₀ cos² θ.
Worked example
In Young's experiment λ = 600 nm, d = 0.50 mm, D = 1.0 m. Find β. β = λD/d = (600×10⁻⁹ × 1.0)/(0.50×10⁻³) = 1.2×10⁻³ m = 1.2 mm. Reasoning: convert nm to m and mm to m; β does not depend on the order n.
Traps
Using the dark-fringe condition for bright fringes; thinking β changes with order; confusing diffraction minima with interference; and forgetting that β decreases in water.