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Diffraction

Diffraction. How do we know light is a wave? Waves undergo diffraction if a wave encounters an object that has an opening of dimensions similar to its  , part of the wave will flare out through the opening can be understood using Huygen’s argument true for all waves e.g ripple tank.

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Diffraction

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  1. Diffraction • How do we know light is a wave? • Waves undergo diffraction • if a wave encounters an object that has an opening of dimensions similar to its , part of the wave will flare out through the opening • can be understood using Huygen’s argument • true for all waves e.g ripple tank

  2. Water waves flare out when passing through opening of width a a 

  3. e.g. sound v=f =v/f = (340m/s)/1000Hz = .34 m a of door ~ 1 m => a~ 3  tangent to wavelets a =4  e.g. light ~ 500 nm = 5 x 10-7 m => need smaller opening

  4. Fresnel Bright Spot Shine monochromatic light on a solid sphere. What image is produced behind it? Geometrical Optics Wave Optics

  5. 1. C close to B no diffraction=>geometrical shadow 2. C very far from B => Fraunhoffer diffraction 3. Intermediate case- rays not parallel => Fresnel diffraction Fraunhoffer diffraction is the easiest to handle

  6. Single Slit Diffraction

  7. Single Slit Diffraction

  8. Assume screen is far enough away that red rays are parallel Path difference between neighbouring rays is z sin Total electric field due to r1 and r2 is E(r1,t)=Em[sin(kr1-t) + sin(kr1-t+k z sin)] z

  9. Single Slit • E(r1,t)=Em[sin(kr1-t) + sin(kr1- t+k z sin)] • where range on z is 0  z  a Phase difference between top and bottom

  10. Single Slit • Amplitude =[2(Em /ksin)sin(kasin/2)] =[2(Ema/)sin(/2)] • = (Ema)sin(/2)/(/2) • I = I0 (sin(/2)/(/2))2 • where I0 = (Ema)2 is the maximum intensity • note: lim sin(x)/x => 1 x => 0 • intensity is maximum at  = 0

  11. Single Slit • I = I0 (sin(/2)/(/2))2 = 0 when /2 = m= asin/ • asin= m for a dark fringe ( m0) • note : m=0 is a maximum! • where are the other maxima? • maximize sin(x)/x with respect to x • (d/dx) [sin(x)/x ] = cos(x)/x - sin(x)/x2 = 0 • or x = tan(x) => x =0 is a solution • plot x and tan(x ) versus x and look for intersections

  12. tan(x)  2 3 x x ~ (m+ 1/2) , m=1,2,3

  13. sin(x)/x [sin(x)/x]2 

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