PA2001: Time and Energy Waves and Interference Light as a wave Fermat’s principle Reflection Refraction Thin Film interference Single slit diffraction Young’s double slit experiment Tipler Chapters 16,33,35 Waves and Interference Dr Mervyn Roy, S6

PA2001: Time and Energy Waves and Interference The Electromagnetic Spectrum 400 nm 700 nm 500 nm 600 nm Wavelength 0.1 nm 1 nm 100 nm 10  m 1 mm 10 cm 10 m 1000 m Long-waves Radio, TV Microwaves Infra-red Visible X-rays Gamma rays

PA2001: Time and Energy Waves and Interference Fermat’s principle The path taken by light in travelling from one point to another is such that the time of travel is a minimum. Explains the law of reflection: Euclid

PA2001: Time and Energy Waves and Interference Phase changes incident wave: wave incident on a barrier

PA2001: Time and Energy Waves and Interference Phase changes wave incident on a barrier phase change of   upon reflection (note: phase change of  only for reflection at rare/dense interface) reflected wave: incident wave:

PA2001: Time and Energy Waves and Interference Refraction some reflection Snell’s Law - derived using Fermat’s principle – shortest path is not the fastest as v < c note: phase change of  only at rare / dense interface rare medium (air) dense medium (glass)

PA2001: Time and Energy Waves and Interference Refraction rare medium (air) dense medium (glass) some reflection Snell’s Law - derived using Fermat’s principle – shortest path is not the fastest as v < c note: phase change of  only at rare / dense interface phase change  no phase change

PA2001: Time and Energy Waves and Interference Refraction 2 Or, why shooting fish in a barrel isn’t easy Fish are always deeper than you think n water = 1.3

PA2001: Time and Energy Waves and Interference Dispersive media - waves of different wavelength travel at different velocity and therefore refract differently © The Exploratorium Newton’s prism

PA2001: Time and Energy Waves and Interference Interference Add coherent harmonic waves with phase difference  0, 2   /2

PA2001: Time and Energy Waves and Interference Interference Add coherent harmonic waves with phase difference  0, 2   /2

PA2001: Time and Energy Waves and Interference Interference Add coherent harmonic waves with phase difference  0, 2   /2

PA2001: Time and Energy Waves and Interference Interference Add coherent harmonic waves with phase difference  0, 2   /2

PA2001: Time and Energy Waves and Interference Interference 2 Add coherent harmonic waves with phase difference Intensity, In general (Hecht, Optics 2nd Ed. 9.1), With constant amplitude as before,

PA2001: Time and Energy Waves and Interference Interference 3 Phase difference is related to path difference Add coherent harmonic waves with path difference,

PA2001: Time and Energy Waves and Interference Thin film interference 1 travels further than difference in path length introduces phase difference interferes with type of interference depends on To find type of interference: Calculate path and phase difference, then: Note: have to be careful with possible phase changes of  at each interface

PA2001: Time and Energy Waves and Interference Thin film interference 2 travels further than difference in path length introduces phase difference interferes with type of interference depends on At normal incidence: Maximum in the intensity if

PA2001: Time and Energy Waves and Interference Thin film interference 3 © The Exploratorium, At normal incidence see interference fringes with films of varying thickness

PA2001: Time and Energy Waves and Interference A B C D Thin film interference 4 B AD A C D combinewith Snell’s law

PA2001: Time and Energy Waves and Interference Thin film growth At fixed, angle of incidence, In-situ monitoring of film thickness

PA2001: Time and Energy Waves and Interference aperture size ~ wavelength screen slit width, a Diffraction (single slit) Water wave © The Exploratorium,

PA2001: Time and Energy Waves and Interference Diffraction (single slit)  a aa aa  a Screen Intensity screen slit width, a Laser light

PA2001: Time and Energy Waves and Interference Young’s slits slit separation, d Laser light Interference fringes Screen far away, rays ~ parallel d Path difference, Constructive interference:

PA2001: Time and Energy Waves and Interference Diffraction gratings © The Exploratorium, Angle of maxima is wavelength dependent: