2. Wave Physics PHYS 2023 Tim Freegarde

3. 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:

4. 3 3 Young’s double slit diffraction x

5. 4 4 x amplitude intensity

6. 5 5 Young’s double slit diffraction x amplitude intensity

7. 6 6 Single slit diffraction x amplitude intensity

8. 7 7 Diffraction grating x m=0 m=1 m=2 m=-1 m=-2

9. 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

10. 9 Diffraction gratings newport.com diffracted angle

11. 10 Grating spectrometer scope.pari.edu

12. 11 Diffraction gratings newport.com diffracted angle incident angle

13. 12 Phased-array loudspeakers Croke Park, Dublin duran-audio.com AXYS incident angle phase angle

14. 13 Phased-array radar Fylingdales, Yorkshire 2560 transducers, 25m diameter, 420-450 MHz phase angle

15. 14 Towed array sonar typically 100 hydrophones over 300m 1500 m.s -1 seawater; 1435 m.s -1 freshwater www.surtass-lfa-eis.com phase angle

16. 15 Spatial light modulators 1920 x 1200 pixels, LCD technology 8.1 μm pitch www.holoeye.com

17. 16 Spatial light modulators 1920 x 1200 pixels, LCD technology 8.1 μm pitch www.holoeye.com laser tweezing of 2 μm glass spheres in fluid computer-controlled hologram www.physics.gla.ac.uk/optics projected and viewed through microscope

18. Wave Physics PHYS 2023 Tim Freegarde

19. 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 http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7 further phenomena and implications

20. 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

21. 20 Diffraction grating x interference by division of wavefront

22. 21 Michelson interferometer interference by division of amplitude beamsplitterdetector source δxδx

23. 22 Michelson interferometer interference by division of amplitude beamsplitterdetector source δxδxδxδx sodium doublet optique-ingenieur.org chemistry.oregonstate.edu FTIR: Fourier transform infrared

24. 23 Beating TWO DIFFERENT FREQUENCIES

25. 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 www.sciencebuddies.org