physics7c-fall06-mt2-Aganagic-exam - (mag > g g 0...

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Unformatted text preview: (mag > g g 0 10} umpmm Xm'puooas ouo [)th ‘P-LEITIIIIUZI 3 3m alaql :910 N) Butyugm [a ngxew (113.00] “01] fimpuoaae (q 12me ([13qu "31) [Edmund (1e 01 Bugpuodsanoo 9 go genre}; mgnagqmd 9111 Jo} 31111213121?) 109qu mug '9 Xm‘quqm we .10} d mgod aq; 119 Sims 9 9ch 111014 snouquuuoa mag agnoela oqq Sunrlasmdal ru'elfi'etp .Iosreqd 13 mag (‘1!) 'srms Bugmqqfi'gou 30 Imd 'P. 10] g eoueiaglp 3:3qu mm umop BJIIM :9 ptm ‘p ‘Y }0 some: 11; gummy); am magma pm; ‘scms sq; mm; Kama 9 913112 II’Q up. US$103 am no d qmod *e no smog 1:331:25 13 ngq 1:31p Sims 3931;; qfinmqq Bugssud m3“ aql, ‘p aau'egsgp 'E! liq pamredas sins 11113013pr [[11le “eggs OJH—qugod g 1gp»: [males 13 U0 11131313111 3! Y qqfillepABm }0 “EH male»qu ' ('0 : 1 91mm ‘laquao 911:1 TE 3110 5; 313g: H) g’xtwoo nqfiq paqlgmsmzn II! ummyupu 1131-5 aq-J, mm 13511133 aqq 11101; 11;} 3501.1 [3 (‘0 z I 33111111 ‘Jaquaa aqq 112 3110 5:1 91011."; H) $111030 1113;] pezoegam In ummguuu 23.11.; 3qu [[Im 131113;) aqg, mm; 13; moH (q astueeq Eugeya'm; 111311913; egg I0; qqfiuaI [mad II; anuamgggp sq; a! 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What are the values of I /I0 for the situations in a), b), and c) of part (iii.) above? (IO is defined to be the intensity at point P from a single slit, that is, the intensity if two of the point-like slits are blocked.) (Hint: look at the phasor diagrams.) (v.) Sketch a graph of the intensity on the screen given your results from above. (vi) Sketch a graph of the intensity if instead the slits are wide (i.e., are not point-like). (The slit width a is still less than the spacing between slits d.) 3. A light source B passes a detector A with speed 1) and then travels away from A in the +x direction. B emits two short pulses of light, the first when A and B coincide (exactly when B passes A) and the second a time At}, later (as measured in B‘s rest frame, 5’) sent in the -x direction (toward A). ‘ a) Draw a spacetime diagram for A’s rest frame, 8. Include and label A’s worldline, B’s worldline, the Worldline of the second light pulse, and the events of the second light pulse being emitted by B and of being received by A. b) Find the time interval AtB between the emission of the two pulses as measured in A’s rest frame, S (in terms of At‘b and 1)). Label (3733 on your diagram from part a). c) Find the spatial separation Ass ,1 of the emission of the bare pulses as measured in A’s rest frame, S (in terms of At’B and 1)). Label AmA on your diagram from part a). d) Find the time interval AtA between the arrival of the two light pulses at A, again in A’s rest frame, S. (Hint: the second pulse travels with speed c.) Write [MA in terms of At:3 and 1). Label AtA on your diagram from part a). 6) By interpreting the 2 pulses as successive crests of an electromagnetic wave, use your result from part d) to derive the relation between the frequency of light received and the frequency of light emitted (i.e., the relativistic Doppler efi‘ect). (The phenomenon that the frequency of omitted and absorbed light are not the same, the relativistic Doppler effect, is fundamentally different from that of sound. For sound waves, one can use the Doppler effect to determine whether it is the source or observer which is moving relative to the medium, air. On the other hand, the relatvitistic effect, which you just derived, cannot be used to determine absolute motion.) 4. A spaceship passes by the Earth with speed 1) in the +x—direction. The proper length of the ship is LP. The spaceship fires three rockets simultaneously in its rest frame: one from the front (event 1), one from the middle (event 2) and one from the back (event 3) of the ship. i.) Draw a spacetime diagram for the rest frame of the earth. Include and label the worldlines of the front, the middle and the back of the ship. Label the three events of the rockets being fired. ii.) Draw the position of the ship at one instant on Earth. What is the ship’s length as measured from Earth? In the Earths rest frame, are events 1, 2, and 3 simultaneous? If not, in which order do they occur? Answer this question using only the spacetime diagram in i). iv.) Using Lorentz transformations, compute the time interval between events 1 and 2 and between events 2 and 3 (in terms of LI] and v) in Earth’s rest frame. Compare to your answer in ...
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physics7c-fall06-mt2-Aganagic-exam - (mag &amp;gt; g g 0...

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