Chapters_27

Chapters_27 - Chapter 27: Wave Optics (interference and...

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1 Chapter 27: Wave Optics (interference and diffraction) Outline ---- 1. Interference pattern: --- Young’s double-slit experiment --- 2. Diffraction pattern : --- single slit experiment --- 3. Multi-slit – diffraction grating --- 4. Resolution of optical instrument 5. Ability to solve real problems d sin θ = m λ , (bright) { (m + 1/2 ) λ , (dark) I difract = I 0 sin 2 ( ) δ 2 ( ) 2 δ 2 interefer d d a a a sin θ = k λ , (dark) { (k + 1/2 ) λ , (bright) l
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2 l l = Observation: the lights pass through the two slits, forming bright and dark lines everywhere on the screen (the center is always bright). 1. Interference pattern (1) Young’s double slit experiment Huygens’s principle
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3 m = 0 m = + 1 m = + 2 m = - 2 m = - 1 --hi, here are what we need to understand: (1 o ) How is the line (or intensity of the line) formed? (2 o ) Why the intensity for the bright lines are NOT the same? – because of the diffraction effect joins in. Pattern intensity I (2) real double slit experiment pattern
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4 (a) constructive and destructive interference Constructive -- (waves 1 and 2 have the same phase) π Destructive -- (waves 1 and 2 have a phase difference of )
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(b) the intensity of the lines -- pure interference pattern: the intensity of each bright line is the same (note: NOT real case) . l L L L L L y E 1 E 2 . tan sin L y = θ , sin 0 1 t E E ω = ), sin( 0 2 d t E E δ + = r 1 r 2 s 2 s 1 d and t kr E E ), sin( 0 1 - = )]. sin( 0 2 d t kr E E - - = , 2 cos ) sin( 2 2 cos ) 2 sin( 2 ) sin( sin 0 0 0 0 2 1 d d d d t E t E t E t E E E E + = + + = + = ( ω ~ 10 15 rad/s for light) ), 2 ( cos 4 2 0 d I I = ]. ) sin ( , [ 2 0 0 2 t E I E I -- hi, you see what: for a wave, a length of λ 2 π , then a length of l d : , 2 d l π λ = , sin 2 2 d l d = = ), sin ( cos 4 2 0 d I I = -- hi, that is the intensity of the lines for pure interference pattern on the screen ! For L >> a (the screen is far away form the slits), i) ii) E 1 and E 2 are essentially parallel, sin d l = where is the phase difference due to the the difference in the path length for the two beams from slits s 1 and s 2 when they reach the screen. [note: one can write them down more generally as
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This note was uploaded on 07/13/2008 for the course PHYS 6C taught by Professor Staff during the Spring '01 term at UCLA.

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Chapters_27 - Chapter 27: Wave Optics (interference and...

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