Synopsis

Waves: The 1-D equation, application to waves on a string, sinusoidal solutions, amplitude, frequency wavelength, energy transport, transverse and longitudinal waves; boundary conditions at free or fixed end; superposition, interference; travelling and standing waves including complex form; plane waves in 2-D and 3-D, the wave vector and wave number.

Optics: Huygens’ Principle, laws of reflection and refraction, lenses, lens formulae, real and virtual images, the simple telescope and microscope.

Diffraction: diffraction using complex amplitudes, Young’s slits and the diffraction grating, finite slit using complex amplitude and via integration.

Quantum waves: reminder of wave-particle duality and de Broglie relation; introduction to the wavefunction and 1-D time independent Schrodinger equation; waves in wells and boxes and quantisation of wavelength; reflection at potential steps; penetration through a barrier and evanescent waves.