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Chapter 19: Interference & Diffraction

Chapter 19: Interference & Diffraction. Honors Physics Bloom High School Mr. Barry Latham. 19.1 Interference. Incoherent light- randomly generated wave fronts Partially out of phase Coherent light- light generated in phase. Young’s Double-Slit Experiment. Interference Fringes

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Chapter 19: Interference & Diffraction

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  1. Chapter 19:Interference & Diffraction Honors Physics Bloom High School Mr. Barry Latham

  2. 19.1 Interference • Incoherent light- randomly generated wave fronts • Partially out of phase • Coherent light- light generated in phase

  3. Young’s Double-Slit Experiment • Interference Fringes • Coherent light shone through a barrier with 2 closely spaced, thin slits produces bright and dark bands • Results from constructive and destructive interference

  4. Young’s Double-Slit Experiment • Interference Fringes • With monochromatic light, the bands are the same color as the source, but are light and dark • With white light, ROYGBIV shows up in the bands

  5. Calculating l • x (or y)- distance from central bright spot to first maximum (m) • d- distance between the slits (m) • L- distance between slits and screen (m) • ml= xmd/L • m- the location of the bright spot (unitless) • 0=central spot • 1=1st spot (left and right of 0) • 2= 2nd spot (left and right of 0)

  6. Practice Problem(find l) • Light falls on a pair of slits 19.0mm apart and 80.0cm from a screen. The first order bright band is 1.90cm from the central bright band. What is the wavelength of light? • l=xd/L • l=(1.90x10-2m)(19.0x10-6m)/(80.0x10-2m) • l=4.51x10-7m = 451nm (high end of blue)

  7. Practice Problem(find x) • Light from a street light of wavelength 596nm is aimed at two slits that are separated by 1.9x10-5m. What is the distance from the central band to the first-order yellow band if the screen is 0.600m from the slits? • l=xd/L  x=lL/d • x=(596x10-9m)(0.600m)/(1.9x10-5m) • x=1.88x10-2m = 0.0188m

  8. Practice Problem(find d) • In a double-slit experiment, a 632.8nm laser is used. The screen is placed 1.000m from the slits and the first-order bright band occurs 65.5mm from the central band. What is the slit separation? • l=xd/L  d=lL/x • d=(632.8x10-9m)(1.000m)/(65.5x10-3m) • d=9.66x10-6m = 9.66mm

  9. Practice Problem(find L) • Light with a wavelength of 596nm passes through two slits that are separated by 0.225mm and makes an interference pattern. If the distance from the central spot to the first-order bright band is 2.00cm, how far is the screen from the slits? • l=xd/L  L=xd/l • L=(2.00x10-2m)(0.225x10-6m)/(596x10-9m) • L=7.55x10-3m = 7.55mm

  10. 19.2 Diffraction • Diffraction pattern- constructive and destructive pattern from the two slit experiment • Single Slit- different l’s produce different effects • Blue light produces narrow bands • Red produces wider bands • Huygen’s wavelets • The gap can be imagined to have act as infinite single-sources of light • Phet.colorado.edu Wave Interference 1.09

  11. Determining band widths • 2xm=2mlL/w • xm=the distance from the central band to the mth dark band (m) • m=1st, 2nd, 3rd… dark band away from the bright central band • l=wavelength (m) • L=distance from slit to screen (m) • w=width of the slit (m)

  12. Practice Problem(find xm) • Monochromatic green light of wavelength 546nm falls on a single slit of width 0.095mm. The slit is located 75cm from a screen. How wide will the central band be? • 2xm=2mlL/w • x1=(2)(1)(546x10-9m)(75x10-2m)/(0.095x10-3m) • x1=0.00862m = 8.62mm

  13. Practice Problem(find L) • Yellow light with a wavelength of 589nm passes through a slit of width 0.110mm and makes a pattern on a screen. If the width of the central band is 2.60x10-2m, how far is it from the slits to the screen? • 2xm=2mlL/w  L=wxm/(2ml) • L=(0.110x10-3m)(2.60x10-2m)/(2x589x10-9m) • L=2.43m

  14. Diffraction Gratings • Made up of many single-slits • Plastic or glass etched with diamonds • Transmission gratings- light shines through • Films used in class • Reflection gratings- light bounces off like a mirror • CD, DVD, Laser Disc • l=(d)sin(q) • Wavelength (l) in meters • Grating spacing (d) in meters

  15. Practice Problem(find d) • If blue light of wavelength 434nm shines on a diffraction grating and the spacing of the resulting lines on a screen that is 1.05m away is 0.55m, what is the spacing between the slits in the grating? • l=(d)sin(q), tan(q)=x/L • q=tan-1(0.55/1.05)=27.64° • d=l/sin(q)=(434x10-9)/sin(27.64°) • =9.35x10-7m

  16. Rayleigh Criterion • A lens acts as a circular single-slit • w is replaced with D (diameter) and a correction factor, 1.22 • xobj=1.22lLobj/D • If the bright band of one star falls on the dark band of another, the two stars are at the limit of resolution • Closest distance that can be determined to be two stars

  17. Intensities from stars • 1- two very distinct stars • 2- one maximum overlaps a minimum • 3- stars too close to tell that they are two stars • http://webphysics.davidson.edu/physlet_resources/bu_semester2/index.html

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