Oscillations, Waves & Optics 2013-14

Dr John RicherPrerequisites

An understanding of waves is fundamental to many areas of physics. This course develops further the ideas presented in the Part IA courses on oscillations and waves, and introduces the theory of diffraction. First, the physics and mathematics of oscillations and waves are revised, and applied to a variety of physical systems. The use of the Fourier Transform as a powerful tool for understanding the behaviour of general linear systems is then introduced, and used to relate the time-domain and frequency-domain behaviour of damped electrical and mechanical oscillators. Finally, these ideas are further developed in the context of classical optics, with particular regard to diffraction and interference phenomena.

Synopsis

**Oscillations:** Driven damped oscillations, frequency response, bandwidth, Q-factor. Impulse response and transient response.

**Waves:** Revision of 1-d wave equation. Waves on a stretched string. Polarisation. Wave impedance. Reflection and transmission. Impedance matching. Compression waves in a fluid. Waves in 2 and 3 dimensions. Standing waves in a box. Wave groups, group velocity, dispersion. Waveguides: cut-off and dispersion.

**Fourier transforms in linear systems**: Linear response and superposition in physics. Fourier series and Fourier transforms. Frequency response as Fourier transform of pulse response. Convolution. Applications to oscillating systems.

**Optics and diffraction:** Huygen’s principle as a solution to the wave equation. Fraunhofer diffraction, Fraunhofer integral, relation to Fourier transform. Wide slit as example of extended source. The width of spectral lines. Gratings and spectroscopy. 2-d apertures, circular apertures, Babinet’s principle. Fresnel diffraction, Cornu spiral, zone plate.

**Interference:** Thin film interference. Fabry-Perot etalon. Michelson interferometer, Fourier transform spectroscopy.