Wave Optics - Quick Revision
Huygens' principle
- A wavefront is a surface of constant phase; energy travels perpendicular to it.
- Every point on a wavefront acts as a source of secondary spherical wavelets; the forward envelope (common tangent) gives the new wavefront.
- Explains reflection and refraction. Wave model predicts the speed of light is less in a denser medium (v = c/n), confirmed by Foucault (1850).
- Refraction: n1 sin i = n2 sin r; frequency stays the same, wavelength and speed change (lambda' = lambda/n).
Interference (Young's double slit)
- Coherent sources keep a constant phase difference; derived from one source (single slit S feeding S1, S2).
- Path difference: delta = d sin theta = x d / D.
- Constructive (bright): delta = n lambda; destructive (dark): delta = (n + 1/2) lambda.
- Bright fringe position x_n = n lambda D / d; fringe width beta = lambda D / d (equal spacing).
- Resultant intensity I = 4 I0 cos^2(phi/2), where phi = (2 pi / lambda) delta. Max = 4 I0, min = 0.
- Incoherent sources: intensities just add (I = 2 I0).
Diffraction (single slit, width a)
- Central bright maximum at theta = 0; minima at a sin theta = n lambda (n = +/-1, +/-2, ...).
- Secondary maxima (weaker) near a sin theta = (n + 1/2) lambda.
- Width of central maximum = 2 lambda D / a (twice the width of side fringes).
- Diffraction sets the resolution limit of eyes, microscopes, telescopes.
Polarisation
- Light is a transverse EM wave; only transverse waves can be polarised.
- A single polaroid transmits half the incident unpolarised intensity (I0/2).
- Malus' law: I = I0 cos^2 theta for plane-polarised light through an analyser.
- Brewster's law: tan i_p = n; reflected light at i_p is fully polarised, and reflected and refracted rays are perpendicular.
Energy
- Interference and diffraction only redistribute light energy (dark vs bright); total energy is conserved.