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MT2 - Physics 7C Midterm 2 Professor Mina Aganagic November...

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Unformatted text preview: Physics 7C Midterm 2 Professor Mina Aganagic November 6, 2007 Please write your discussion SECTION NUMBER on your blue book (or meeting day and hour if you don’t remember the section number). Please put all answers in Blue Books. " 1 30 [0+5 Coherent plane wave of wavelength A is incident on 3 equally spaced point—like slits, with adjacent slits separated by a distance d. The light passing through these slits then hits a screen far away. Focus on a point P on the screen at an angle 0 from the slits, and answer the following in terms of A, d, and 0. a. Write down the phase difference, 6, for a pair of neighboring slits as a function of d, A and 0. b. Draw a phasor diagram representing the electric field contributions from the 3 slits at the point P for an arbitrary 0. c. Draw the phasor diagram for particular values of 6 in the range [0, 27r), corresponding to i. principal (i.e. global) maxima ii. minima (Hint: there are 2 minima for 0 g 6 < 27r.) iii. secondary (i.e. local) maxima (Hint: between the minima there should be a maximum.) d. What are the values of I / L, for the situations 1', ii, iii where I is the net intensity for the corresponding 6, and L, is defined to be the intensity due to a single slit. e. Sketch a graph of the intensity on the screen as a function of 6 in the range of [—27r, 2%] given your results from above. 2 38 F‘I'J' Consider an experiment where you are smashing protons against anti—protons, in hope these will bind to make a short lived particle of a particular kind. The mass, m, of a proton is the same as the mass of an anti-proton, m = lGeV/c2. a. In experiment A, you accelerate an anti—proton to kinetic energy AA, and smash it against a proton which is at rest in the lab. Assuming the proton and anti—proton bind, find how the mass M of the resulting particle depends on AA, and m. What AA do you need to produce a particle, the so called J—psi, that has mass M = 3GeV/c2? b. In experiment B, both the proton and the anti-proton are accelerated, towards each other, so that each carry half of total kinetic energy AB. Find how the mass M of the resulting particle depends on A3 and m now. What AB do you need to produce a J-psi particle in experiment B? c. In an accelerator, the net kinetic energy required translates directly into the cost of experiment. Which is the more cost effective experiment, A or B? 3 ES [07‘s A space-ship moves towards planet Z, with speed I) in the +x direction as shown in the figure. The proper length of the spaceship is Lp- The spaceship fires two laser pulses towards planet Z simultaneously in the spaceship’s rest frame. One pulse is fired from the front of the ship (call this event 1), and one from the back (call this event 2). ’6 P’Qnti‘z' Figure 1: a. Draw a spacetime diagram for the rest frame of planet Z. Include and label the worldlines of the front, and back of the ship. Also draw the worldline of planet Z, idealized as having no spatial extent. b. On the diagram from part a, label events 1 and 2 (the precise location of the ship corresponding to this will be irrelevant for the problem). Label the events of the light pulses hitting planet Z (call this events 3 and 4). c. In planet Z’s rest frame, are events 1, and 2 simultaneous? If not, in which order do they occur? Answer this question using only the spacetime diagram in (a). d. Using Lorentz transformations, compute the time interval between events 1 and 2 (in terms of LI, and v) in planet Z’s frame. Compare to your answer in (c). e. Find the time interval, in the Z’s rest frame between two pulses hitting planet Z (events 3 and 4). f. Find the time interval between events 3 and 4 in the ship’s rest frame. ...
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