Optics

School optics treats light as rays that bounce and bend. University optics takes the wave seriously — and once you do, light does things rays never could. Two beams can add up to darkness. A sharp edge casts a fringed shadow. A single slit smears a point of light into a pattern that is nothing less than the Fourier transform of the slit itself.

This branch is physical optics: Huygens' principle, interference and diffraction done properly, coherence and the interferometers that measure a wavelength of a metre-long baseline, polarisation and its elegant matrix algebra, and the laser — light made orderly. It builds on waves and the Fourier methods in mathematics.