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PH 103

PH 103. Dr. Cecilia Vogel Lecture 8. Review. diffraction interference coherence. Diffraction/interference examples double - slit and diffraction grating single slit thin films holograms. Outline. Two-slit interference. AKA Young’s experiment

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PH 103

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  1. PH 103 Dr. Cecilia Vogel Lecture 8

  2. Review • diffraction • interference • coherence • Diffraction/interference examples • double-slit and diffraction grating • single slit • thin films • holograms Outline

  3. Two-slit interference • AKA Young’s experiment • Two waves start out in phase, but one travels farther • one wave gets behind (analogy: cars) • Geometry: slits Observation screen 

  4. Two-slit interference • Geometry if slits d and l << L • difference in distance traveled = • dsinq • or dy/L

  5. Two-slit interference • Constructive interference if difference in distance traveled = integer # of wavelengths • dsinq= ml • or dy/L = ml • Destructive interference if difference in distance traveled = (integer-1/2)wavelengths • dsinq= (m - ½)l • or dy/L = (m - ½)l

  6. Two-slit interference • Bright fringes: dy/L = ml • distance between fringes: dDy/L = l • How does interference pattern depend on • slit separation? • Larger d, smaller Dy -- fringes closer • wavelength? • Longer l, larger Dy -- fringes farther • longer wavelengths diffract more • interference can tell yellow from red +green • material? l = lo/n, shorter l

  7. Many-slits = diffraction grating • Each pair of slits behaves like double-slit • Constructive interference if • dsinq= ml • or dy/L = ml • Destructive interference if • dsinq= (m - ½)l • or dy/L = (m - ½)l • Fringes are in same place as double-slit, but sharper

  8. Many-slits = diffraction grating • How far apart are the slits? • Suppose the are 10 lines/cm, then there is one line in 1/10 cm = 0.1 cm • the lines are 0.1 cm apart • generally d = 1/(number of lines per unit length)

  9. Single Slit diffraction pattern • Dark Fringes occur at (m =integer again) • So, width of center bright spot, qcenter • How does pattern depend on • slit width • narrower slit causes more diffraction & wider pattern • wavelength • longer wavelengths diffract more

  10. One-slit/Two-slit Confusion • Note: W=slit width, but d=slit separation • Is the spot bright or dark? • Single-slit eqn is for dark (destructive interference) • Double-slit eqn is for bright (constructive interference) • What values of m are possible? • M = all integers for double slit • m = integers except zero for single slit Single-slit Double-slit

  11. Circular opening diffraction pattern • Circular diffraction pattern depends on • Aperture radius, a • smaller - more diffraction & wider pattern • wavelength • longer wavelengths diffract more • So two objects separated by ½ that can be resolved as separate bright spots = “Rayleigh Criterion”

  12. Hologram • Light wave split in two by half-silvered mirror • One part shines on object, then reflects to film = “ object beam“ • one part goes directly to film = “reference beam“ • Interference of these two waves depends on how much further one travels than the other • 3-D shape of the object recorded as • Developed film is like a complicated grating • When light falls on film, reproduces light from original object

  13. One more thing about Reflection • Wave will change phase by 180o (i.e. ½l) if it reflects from material where the wave goes slower (higher n) • Wave will not change phase if it reflects from material where the wave goes faster (lower n) Demo

  14. VERY Thin film • When light strikes a thin film at small incident angle, some reflects from top surface, some from bottom surface. • If the film is very thin, the only difference between the two reflected waves is if one has a phase change when it reflects. • Does each wave experience a phase change?

  15. VERY Thin Films • Constructive interference if both or neither change phase • light comes from the smallest n, film is intermediate • or light comes from largest n, film is intermediate • Destructive interference if • film is largest n • or film is the smallest n

  16. Thin Films • The two waves also differ in distance traveled by twice the thickness = 2t • If difference in distance traveled is integer number of cycles, then • same result as very thin film • beware: wavelength within film (use n of film) • 2t = m l/n • If difference in distance traveled = integer number of cycles + ½ cycle, then • opposite result from very thin film • again beware: wavelength within film • 2t = (m+½) l/n • Must know what happens to very thin film 1st!

  17. EXAMPLE Antireflective coating: Thin coating of material with n=1.25 on glass (n=1.55) makes 525-nm green light not reflect. How thick should the coating be? 1st: What happens when light from air hits a very thin film like this? n of film is intermediate, so it would be bright. 2nd: To make it dark instead (opposite), it must travel through a thickness given by: 2t = (m-½) l/n t = (m-½) l/2n=(½)(525nm)/(2(1.25)) = 105 nm =1050 Å

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