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Unformatted text preview: Physics 70 Section 2
Spring 2005
Midterm II, April 5, 2005
Prof. Marco Battaglia Choose four out of the ﬁve proposed problems. The test duration is 110 minutes. 1. The Fresnel equation gives the reﬂection coefficient R“ for waves parallel to the plane of incidence as R“ = :2: 31:43: , where the angles of incidence 91 and refraction 02 are deﬁned by the Snell’s law. 1) Derive the analytic expression of the Brewster’s angle, at which the reﬂected light is fully
polarised in the plane perpendicular to the plane of incidence.
2) Find the value of the Brewster’s angle for light reﬂected from a water surface. 2. A B particle, with mass=5.2 GeV/c2, is produced with a momentum p$=40 GeV / c. 1) Compute the value of 7 for the B particle. 2) The decay generates two identical pion particles, 7r, each with mass=0.14 GeV/c2, such that
the momentum of one of the pions,‘ in the decaying B rest frame, projected along the line of ﬂight
of the B in the lab, is pay 122 GeV/c. Compute the angle between the two pions both in the B
particle frame and in the laboratory frame. Do these angles depend on pm: 1 ? 3. A cosmic ray eihseriment is conducted using two detectors: the ﬁrst is located at an altitude
of 2000 m and the second at 500 m. The ﬁrst detector counts 550 muons/hour and the second
400 muons / hour. The difference in counts is entirely due to the decay of muons according to the
exponential law I (t) = I (0)?” T. The decay time T for muons has been measured to be 2.25 us,
its mass is M# = 0.105 GeV/cz. 1) Determine the speed of the muons assuming Galilean relativity and comment whether the result
is acceptable. _ 2) Determine the energy of the muons using the relativistic prescriptions. (Assume the mucus to travel along a" trajectory normal to the earth surface and, for point 2),
approximate the muon velocity with c in computing the transit time). 4. The relation E = mc2 suggests that a photon 7 of sufﬁcient energy E, = hl/ can generate an
e‘e+ electronpositron pair. 1) Can the pair creation process occur in vacuum (justify the answer) ? 2) Which is the minimum E.) for it to occur with an electron e as spectator: we ——> e+e"e ? 3) Which is the minimum Ely for it to occur with a nucleus N as spectator: 7N —> e+e’N ?
(Assume the spectator to be at rest in the laboratory). 5. The light emitted by the SSA12 galaxy is measured in a spectrometer at the Keck II telescope.
The A=1216 Angstrom Lya H line is observed at a wavelength of 8185 Angstrom. 1) Determine the 2 value for the redshift of the galaxy and its recessional velocity in units of c. 2) Estimate the resolving distance for two stars in this Galaxy emitting light at A=1216 Angstrom,
knowing that the diameter of the telescope mirror is 10 m. (1 Angstrom = 10‘10 m, 1 ly = distance covered by light in one year. Take H0 2 20 km s'1 Mly"1
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