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a; sagsﬂqd (iv.) 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 pointlike 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 pointlike).
(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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 Fall '08
 LIN
 Physics

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