Wave Physics PHYS 2023 Tim Freegarde

2 Wave propagation in changing media Huygens’ constructiongradual change: refraction refraction; continuity conditionsobstacles:1-D: boundary conditions2/3-D: diffraction today’s lecture: interface between media:

3 3 Young’s double slit diffraction x

4 4 x amplitude intensity

5 5 Young’s double slit diffraction x amplitude intensity

6 6 Single slit diffraction x amplitude intensity

7 7 Diffraction grating x m=0 m=1 m=2 m=-1 m=-2

8 8 Diffraction grating x place secondary sources along wavefront...and trigger when wavefront arrives apply to sinusoidal waves by taking into account the phase with which components arrive combine by adding the amplitudes contributions may therefore interfere constructively or destructively INTERFERENCE

9 Diffraction gratings newport.com diffracted angle

10 Grating spectrometer scope.pari.edu

11 Diffraction gratings newport.com diffracted angle incident angle

12 Phased-array loudspeakers Croke Park, Dublin duran-audio.com AXYS incident angle phase angle

13 Phased-array radar Fylingdales, Yorkshire 2560 transducers, 25m diameter, MHz phase angle

14 Towed array sonar typically 100 hydrophones over 300m 1500 m.s -1 seawater; 1435 m.s -1 freshwater phase angle

15 Spatial light modulators 1920 x 1200 pixels, LCD technology 8.1 μm pitch

16 Spatial light modulators 1920 x 1200 pixels, LCD technology 8.1 μm pitch laser tweezing of 2 μm glass spheres in fluid computer-controlled hologram projected and viewed through microscope

Wave Physics PHYS 2023 Tim Freegarde

18 Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS wave equations, derivations and solution sinusoidal wave motions complex wave functions WAVE PROPAGATION Huygens’ model of wave propagation interference general wave phenomenaFraunhofer diffractionlongitudinal waves BEHAVIOUR AT INTERFACES continuity conditions boundary conditions SUPERPOSITIONS linearity and superpositions Fourier series and transforms FURTHER TOPICS waves from moving sources operators for waves and oscillations waves in three dimensions further phenomena and implications

19 Wave propagation in changing media Huygens’ constructiongradual change: refraction refraction; continuity conditionsobstacles:1-D: boundary conditions2/3-D: diffractioninterface between media: place secondary sources along wavefront...and trigger when wavefront arrives apply to sinusoidal waves by taking into account the phase with which components arrive combine by adding the amplitudes contributions may therefore interfere constructively or destructively INTERFERENCE

20 Diffraction grating x interference by division of wavefront

21 Michelson interferometer interference by division of amplitude beamsplitterdetector source δxδx

22 Michelson interferometer interference by division of amplitude beamsplitterdetector source δxδxδxδx sodium doublet optique-ingenieur.org chemistry.oregonstate.edu FTIR: Fourier transform infrared

23 Beating TWO DIFFERENT FREQUENCIES

24 Newton’s rings diffuser beam-splitter lens plate apply to sinusoidal waves by taking into account the phase with which components arrive combine by adding the amplitudes contributions may therefore interfere constructively or destructively