Chapt21_22_VG - Chapters 21 & 22 Interference and Wave...

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Interference and Wave Optics Waves that are coherent can add/cancel Patterns of strong and weak intensity
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Approximate Electric Field: E ( r , t ) = A ( r )cos( kr ω t + θ ) Single Spherical Source Field depends on distance from source and time. A ( r ) 1/ r Typically Most important dependence is in the cosine
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E ( r , t ) = A ( r 1 )cos( kr 1 ω t + φ 1 ) + A ( r 2 )cos( kr 2 ω t + φ 2 ) Two sources that have exactly the same frequency. “Coherent r 1 r 2 Sources will interfere constructively when kr 1 + φ 1 ( ) kr 2 + φ 2 ( )= 2 π m Sources will interfere destructively when kr 1 + φ 1 ( ) kr 2 + φ 2 ( )= 2 π m + 1 2 m = 0,1, 2, . ..
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( r , t ) = A ( r 1 )cos( kr 1 ω t ) + A ( r 2 )cos( kr 2 ω t ) Field and Intensity far from sources* suppose A ( r 1 ) = A ( r 2 ) E ( r , t ) 2 A cos( k Δ r 2 )cos( k r ω t ) Trigonometry cos( A ) + cos( B ) = 2cos( A + B 2 )cos( A B 2
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Chapt21_22_VG - Chapters 21 & 22 Interference and Wave...

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