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 ◦ Coherent light shone through a barrier with 2 closely spaced, thin slits produces bright and dark bands ◦ Results from constructive and destructive interference

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

Calculating Calculating 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) m = x m d/L ◦ m- the location of the bright spot (unitless) ◦ 0=central spot ◦ 1=1 st spot (left and right of 0) ◦ 2= 2 nd spot (left and right of 0)

Practice Problem(find ) Light falls on a pair of slits 19.0  m 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? =xd/L =(1.90x10 -2 m)(19.0x10 -6 m)/(80.0x10 -2 m) =4.51x10 -7 m = 451nm (high end of blue)

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

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? =xd/L  d= L/x d=(632.8x10 -9 m)(1.000m)/(65.5x10 -3 m) d=9.66x10 -6 m = 9.66  m

Practice Problem(find L) Light with a wavelength of 596nm passes through two slits that are separated by  m 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? =xd/L  L=xd/ L=(2.00x10 -2 m)(0.225x10 -6 m)/(596x10 -9 m) L=7.55x10 -3 m = 7.55mm

19.2 Diffraction Diffraction pattern- constructive and destructive pattern from the two slit experiment Single Slit- different ’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

Determining band widths 2x m =2m L/w ◦ x m =the distance from the central band to the m th dark band (m) ◦ m=1 st, 2 nd, 3 rd … dark band away from the bright central band ◦ =wavelength (m) ◦ L=distance from slit to screen (m) ◦ w=width of the slit (m)

Practice Problem(find x m ) 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? 2x m =2m L/w x 1 =(2)(1)(546x10 -9 m)(75x10 -2 m)/(0.095x m) x 1 = m = 8.62mm

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 -2 m, how far is it from the slits to the screen? 2x m =2m L/w  L=wx m /(2m ) L=(0.110x10 -3 m)(2.60x10 -2 m)/(2x589x10 -9 m) L=2.43m

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 =(d)sin(  ) ◦ Wavelength ( ) in meters ◦ Grating spacing (d) in meters

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? =(d)sin(  ), tan(  )=x/L  =tan -1 (0.55/1.05)=27.64° d= /sin(  )=(434x10 -9 )/sin(27.64°) ◦ =9.35x10 -7 m

Rayleigh Criterion A lens acts as a circular single-slit ◦ w is replaced with D (diameter) and a correction factor, 1.22 ◦ x obj =1.22 L obj /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

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 _semester2/index.html _semester2/index.html