Wave Optics
Wave Optics in the HSC paper tests Huygens' principle, Young's double-slit interference, diffraction at a single slit, polarisation by reflection and the resolving power of optical instruments. Fringe-width numericals are almost guaranteed.
Core rules
- Huygens: every point on a wavefront acts as a secondary source; the envelope of secondary wavelets gives the new wavefront.
- Young's experiment: path difference = d sinθ; constructive for nλ, destructive for (n + ½)λ.
- Fringe width W = λD/d, where D is the slit-to-screen distance and d the slit separation. Angular width is λ/d.
- In a medium of refractive index n, λ becomes λ/n and the fringe width shrinks by the same factor.
- Single-slit diffraction: minima at d sinθ = nλ, central maximum twice as wide as the secondary maxima; intensity falls off rapidly.
- Polarisation proves light is transverse. Brewster's law: tanθ(p) = n, and the reflected and refracted rays are perpendicular.
- Resolving power of a telescope = D/1.22λ; of a microscope = 2n sinβ/λ.
Worked example
In a double-slit experiment, λ = 600 nm, D = 1.0 m, d = 0.5 mm. Then W = (600×10⁻⁹ × 1.0)/(0.5×10⁻³) = 1.2×10⁻³ m, that is 1.2 mm. Immersing the apparatus in water (n = 4/3) reduces the width to 0.9 mm.
Traps
- Using D and d in different units; convert both to metres first.
- Assuming fringe width changes with slit width rather than slit separation.
- Believing polarisation can be shown with longitudinal waves; only transverse waves polarise.