Syllabus
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
Problems
From the II Estonian-Finnish Olympiad in Physics (2004)
Problem 4