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Unformatted text preview: The diagram below shows the wave crests for two sources that are totally out of
phase. For each of the labeled points, determine whether the light intensity (not the
wave amplitude) is a minimum or a maximum. Solution: The light intensity (i.e., the brightness) will be largest wherever there is
constructive interference, and smallest wherever there is destructive interference.
Point C in the diagram is located where wave crests from both sources overlap, so
this will be an intensity maximum. Point B will also be an intensity maximum,
because it sits where the wave troughs overlap. (This is why the problem warned
about using intensity rather than amplitude.) At point A, the crest from source 2 overlaps a trough from source 1, resulting in
destructive interference and thus an intensity minimum. Note that this diagram is a snapshot of one instant in time as the waves move
outward from the sources. Onehalf period after this instant, point B will see two
crests and point C will see two troughs, and they will thus still be locations of
constructive interference. The headlights of a pickup truck are 1.32 m apart. What is the greatest distance at which these headlights can be resolved as separate points of light on a photograph taken with a camera whose
aperture has a diameter of 12.5 mm? (Take A = 555 am.) Solution: Picture the Problem: Light that has a wavelength ot‘SSS nm passes through the Iiimm apenure ol'a camera from
two headlights that are .33 m apart. Strategy: Solve equation 38 H for the minimum resolution angle for the given wavelength and aperture sue. then use
equation 283 to calculate the maximum distance ti.) at which the two headlights can be resolved. ' A, , I 555 nm 1 1 .  . '. t . . I' ‘ '"tli‘: U_ :_'im I! }_5]' ‘ ‘lUiUJlU
holutlon. l. { aILulate the resolullutl d a L ....1 ‘I 1‘ D \ 115 mm J
2. IL‘aleulate the maximum distance to the lights: t' — t'. lanHmm I, _ .t' _ L33 I11 : tan Hm... _ [an “.003 It)“ Insight: the ear must he about IS. miles away belin'e the headlights appear to merge. Ihis. ot course. ts the ideal cane.
lo the real world. the ﬁnite size ol‘the headlights and atmospheric distortions greatly reduce this maumum tllﬁtaltlue. A diﬂi'aetion grating has 2200 linestem. What is the angle between the ﬁrst—order maxima for red
light (it. = 53!] um} and blue light (.3. = 4H]I run)? Solution: F'H'IIHI.‘ [ht l'ruhlrm: HE": l'llliln'l'iilll mild hILILIllll lll.'ll ligltl “air Ema l'r.I __! I Flcllll": 't'tiln :'_"l lll‘lt't .'lll “Hum: ‘tIl tetraI‘— IIII "H II': Ir tr!. .Illj. t. I l'::: Iir~I.'rtet mat Ir.! a: 1'..'l." ''.'I.'l.'llt_'l' lHuiante". the hIIIL'viHLJIL'
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 Spring '08
 SEATON

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