Syllabus

http://ipho.org/PDF/2015-12-06%20%20Syllabus%20of%20IPhO.pdf

Plan to briefly discuss portions in bold

2.4.2 Waves

Propagation of harmonic waves: phase as a linear function of space and time; wave length, wave vector, phase and group velocities; exponential decay for waves propagating in dissipative media; transverse and longitudinal waves; the classical Doppler effect. Waves in inhomogeneous media: Fermat’s principle, Snell’s law. Sound waves: speed as a function of pressure (Young’s or bulk modulus) and density, Mach cone. Energy carried by waves: proportionality to the square of the amplitude, continuity of the energy flux.

2.4.3 Interference and diffraction

Superposition of waves: coherence, beats, standing waves, Huygens’ principle, interference due to thin films (conditions for intensity minima and maxima only). Diffraction from one and two slits, diffraction grating, Bragg reflection.

2.4.4 Interaction of electromagnetic waves with matter

Dependence of electric permittivity on frequency (qualitatively); refractive index; dispersion and dissipation of electromagnetic waves in transparent and opaque materials. Linear polarisation; Brewster angle; polarisers; Malus’ law.

2.4.5 Geometrical optics and photometry

Approximation of geometrical optics: rays and optical images; a partial shadow and full shadow. Thin lens approximation; construction of images created by ideal thin lenses; thin lens equation . Luminous flux and its continuity; illuminance; luminous intensity.

2.4.6 Optical devices

Telescopes and microscopes: magnification and resolving power; diffraction grating and its resolving power; interferometers.

Brief notes

Wave equation is a second-order linear partial differential equation. In one spatial dimension, it takes the form \(\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2}\), where \(u=u\left(x,t\right)\) is the scalar quantity that depends on the space and time coordinates. Here, \(c\) is the speed of the wave. (This is actually the phase velocity.)
Phase of a wave

Also refer to notes by Jaan Kalda

https://www.ioc.ee/~kalda/ipho/waveopt.pdf

Problems

From the II Estonian-Finnish Olympiad in Physics (2004)

Problem 4