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class20lecnotes-1 - Class 20 Friday Reading J 2 1 p!C c&...

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Class 20, Friday, February 25, 2010 Reading: J 2, 1. p, !C c. & jC 1 J] 2. ] What do you expect the intensity of the light on the screen to be? Twice that of each individual source, three times, four times? The intensity of a wave is proportional to its amplitude squared. I=Ca 2 Here C is a constant Each source contributes the same amount, Il=I2=Ca~fo. We could perhaps imagine that the intensity of light on the viewing screen should be something like twice the intensity of each individual source, so IlIlf=21o. We now know, however. that the intensity of light on the screen is not homogenous. It varies periodically between bright and dark fringes. Without intenerence, the intensity on the screen would indeed be 210 (if we neglected the effect of the inverse-square-Iaw, by which the intensity of light decreases as the inverse of the distance squared from the source ). So what is it actually? We derived the amplitude of the interfering waves to be: f}:. /2a. 01') I¥) / fJcp=- => ~ ~::: .!f'. d'/Ift & //i1 t7 !::! liM (J.!::!. tJ /AM&:' ~ , L => =) The above formula tells us that the intensity on the screen varies periodically, as we expected. . Ii Iku. )( .c 2. a. I /I IKrh:::' 0 "d. /
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Does this mean that on the screen, the intensity is four times that of one source? Since intensity is related to power and power to energy. this would mean that the law of energy conservation would be violated in this case. This is impossible! How can we resolve this dilemma? The intensity is 410 only at the locations of the bright fringes. In between it is O. We must average over the entire pattern in order to find the intensity on the screen. The average of cos 2 over 2n; is 112. Hence. the average intensity on the viewing screen is. indeed. 210. and energy is conserved. The light from the bright fringes varies between 210 and 410, while the intensity of the dark fringes varies between 0 and 210. OUf considerations so far imply that the intensity pattern on the screen is periodic. with the maximum'intensity being constant as we move away from the central maximum, as indicated in the figure below. In reality, as you will see in your lab. the intensity decreases away from the central maximum. The central maximum is the brightest. Fringes far away from it are dimmer. This is because the intensity is a varying function of distance.
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class20lecnotes-1 - Class 20 Friday Reading J 2 1 p!C c&...

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