Physics · Ch 10 — Wave Optics

Summary

Huygens' Principle: Every point on a wavefront acts as a source of secondary spherical wavelets; the new wavefront is the envelope of these wavelets.
Interference: Superposition of two coherent waves gives intensity $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \delta$ , where $\delta$ is the phase difference.
Young's Double-Slit Experiment: Fringe width $\beta = \frac{\lambda D}{d}$ ; for bright fringes, path difference $\Delta x = n\lambda$ , for dark fringes $\Delta x = (2n+1)\frac{\lambda}{2}$ .
Diffraction: Bending of light around obstacles; single-slit minima occur at $a \sin \theta = n\lambda$ ( $n = \pm 1, \pm 2, \dots$ ), with central maximum width $= \frac{2\lambda D}{a}$ .
Resolving Power: For a telescope, $R = \frac{1}{\Delta\theta} = \frac{a}{1.22\lambda}$ ; for a microscope, $R = \frac{2\mu \sin\theta}{\lambda}$ .
Polarisation: Light waves are transverse; unpolarised light becomes polarised by reflection (Brewster's angle: $\tan i_B = \mu$ ), or by transmission through a polaroid.
Malus' Law: Intensity of polarised light after an analyser: $I = I_0 \cos^2 \theta$ , where $\theta$ is the angle between transmission axes. …