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Unformatted text preview: There are 100 points on the exam. One sheet of notes and a calculator are allowed. Write Physics 70 (Optics and Modern Physics) Second Midterm, Spring 2005 (Wohl) University of California, Berkeley everything on these pages. BOX YOUR ANSWERS. Your name: Your student ID number: Your discussion section number: TOTAL (10 ptS)
(20 pts)
(20 pts)
(15 pm)
(20 pts)
(15 ptS) (100 pts) 1. ( 10 pts) The parts are independent. (a) Four sheets of (ideal) polaroid are stacked with the transmission axes of the second,
third, and fourth sheets oriented at angles 30°, 60°, and 90° to the axis of the ﬁrst sheet.
If unpolarized light of intensity Io is incident normally upon the ﬁrst sheet, what intensity
emerges from the fourth sheet? (b) The setting sun shines from the west. You look up at the (clear) sky directly
overhead through a sheet of polaroid. Which orientation of the transmission axis lets more
light reach your eye? (Minus three points for wrong answer.) @ Circle one: northsouth, eastwest. (c) A birefringent material such as quart or calcite has two indices of refraction: When
the electric vector oscillates perpendicular to the optic axis of the material (shown as 0.4
in the ﬁgures), the index is n _L; when it oscillates parallel to 0A, the index is n“. The ﬁgures show two ways to separate unpolarized light into two beams of linearly
polarized light. Each arrangement uses two prisms of the same birefringent material.
( g Which is the larger index here? (Minus three points for wrong answer.) F! 2 Circle one: n_L > n”, n" > n; . wan/lg. Ms, ) @0A
3': (a) Wolaston prism I (bl Rochon prism 2. (20 pts) (a) Use the ﬁgure to derive the diﬁraction pattern 1(6) when light of wavelength
A is incident upon a slit of width a: ' . 2
@ 1(9) = I(O°) (Eng—£22) . , Deﬁne ,B in terms of A, 0, and a. L
L/ (b) The ﬁrst minimum of a diffraction pattern is at 9 = 4°. Sketch the phasor diagrams ', 3,
for 9 = 0° and 4°. What is the value of a/A. . (c) The slit width is now reduced to a/2. Sketch the phasor diagrams, to the same
@ scale as in part (b), for 9 = 0° and 4°. What are the intensities I’ (0°) and I’ (4°) compared
with the intensity I (0°) when the slit width was a? 3.‘ (20 pts) A thin spherical shell of radius a and negligible heat capacity is a perfect
blackbody emitter. It is ﬂoating far out in empty (T = 0) space, and at time t = 0 it is
ﬁlled with electromagnetic radiation at absolute temperature To. The problem is to ﬁnd
the temperature of the sphere of radiation at later times. (a) What is the total electromagnetic energy E = E(c, a, a, T) in the sphere when it
is at temperature T? Here a is the StefanBoltzmann constant. (b) What is the rate dE/dt at which the sphere loses energy when its temperature is ,
T? (c) Thus get an expression of the form dE / E = f (c, a) dt, Where f (c, a) is a function
of c and a. (d) Thus ﬁnd T(t) for t > O. V4 4. (15 pts) A muon is created by the decay of a pion at an altitude of 30 km above sea
level. The muon travels straight down and decays at sea level after a time, as measured in
its own rest frame, of 2 x 10'6 5. What is the speed of the muon? Or rather, since the answer is very close to c, what
is c — v (to three places), in m/s? Take c to be 3 x 108 m/s. 5. (20 pts) Police in a car going at speed c/ 2 ﬁre shots at outlaws ﬂeeing at speed 3c/4,
both speedsbeing with respect to the ground. The bullets travel at speed c / 3 with respect to the police car. é (a) Do the bullets reach the oulaws according to Galileo?
/ (b) Find the speed of the bullets with respect to the ground according to Einstein.
"Do the bullets reach the outlaws? (c) Find the speed of the outlaws with respect to the police. Is your result consistent
with your conclusion in (b)? 6. (15 pts) A photon collides with an electron and produces an electron—positron pair: 7e‘ ——> e‘e‘e+. Find the minimum (“threshold”) energy of the photon needed to make this reaction “go.”
Give the answer as a multiple of the electron massenergy mcz. (The masses of the electron
and positron are identical.) ...
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