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Unformatted text preview: Physics 171.102 Exam 3 Solutions Nov. 18, 2004
Prof. Barnett Write your TA’s name and your name on each blue book. Write everything in ink.
You may use material written on ONE 3”x5” index card. c = 3 X 108 m/sec. rad
1. The adjacent ﬁgure shows a sinusoidal power supply, Wt) : 4C05(104§e_c t) volts V(t) = 4cos(104%% 75) volts, with a circuit containing (: l a resistor, R = 50 Q, and capacitor, C : ZuF. A) (5 pts) What is the impedance of the resistor? Z325OQ. /\/\/ l I B) (7 pts) What is the impedance of the capacitor? R z 50 Q C = QIIF
w = 104% ZC = 1/z'wC' = —507; o. C) (9 pts) What is the rationalized current phaser for the circuit?
The resistor and capacitor are in series.
ZTOTAL = ZR + 20 = 50(1 — on = soﬁe—ior/og
[(75) = V(t)/ZTOTAL = 4em/(50x/ie‘i("/4l) : 0.057ei(wt+7r/4)amp3
= 0.057ei(104t+"/4) amps. D) (9 pts) What is the rationalized potential phaser for the capacitor?
V005) = I(t)ZC = (0.057ei<1°‘t+"/4> amps)(—50i§l) = ~2.85ei<104t+3"/4> Volts.
= 2.85ei<1°4t-"/4> Volts. 2. Two identical thin converging lenses have focal lengths of f = +2 meters. They are
aligned with each other such that they are 4 meters apart. A candle, 5 cm tall, is
placed 6 meters to the left of the left hand lens. f __= +2 m A) (8 pts) Where is the image formed by the
left lens located relative to the left lens?
—1/S+ 1/S’= 1/f
S=—6m,f=+2m—>S’=3m. The image formed by the left mirror
is 3 meters to the right of it. B) (8 pts) Where is the image formed by the
combined left and right lenses located
relative to the right lens? #1/S + 1/S’ = 1/f S = ——1m,f = +2m —> S’ = —2m.
The image formed by the right mirror
is 2 meters to the left of it. C) (9 pts) Is the ﬁnal image real or virtual, upright or inverted?
What is the magniﬁcation for the complete lens system?
The ﬁnal image is virtual and inverted. T
The magniﬁcation for the left lens isML :' ‘/~S ‘: —1/2 ﬁnal image
The magniﬁcation for the right lens 18 MR 2 S’/S = 2. . t l
The overall magniﬁcation is MT 2 iMLMR = —1.0. 'v1r ua
inverted 3. A glass—covered mirror, nglass = 1.50, has a thin ﬁlm, nfilm = 1.70, on its front to
minimize light reﬂected at normal incidence from the ﬁrst glass surface, as in the
diagram below. Assume that the wavelength of light in air, nm 2 1.00, is 680 nm. A) (8 pts) What phase change occurs duevto the reﬂections
from the ﬁrst and second surfaces of the thin ﬁlm?
n“, < nfum > nglm. There are 7r radians phase change in
the reﬂection from the air/ ﬁlm surface, and no phase
change in the reﬂection from the ﬁlm/ glass surface. B) (8 pts) What phase change occurs due to the light’s traveling in the thin ﬁlm?
For a ﬁlm thickness d, the phase change due to two traversals (to left and back
to right) of the ﬁlm is
Q3 2 27T(2d)/)\film = 47rdnfﬂm/Aair Z 6.87I'd/Aair. C) (9 pts) What is the minimum ﬁlm thickness which will eliminate the reﬂection?
The total phase change for ray 1 is (251 = 7r.
The total phase change for ray 2 is ab = 6.87rd//\a,-,.
For destructive interference $2 — (151 = 7r —> d = 200 nm. 4. Two clocks are approaching you, one from the left and One from the right, both with
speeds of 80% the speed of light. When they were manufactured their dimensions were
10 cm wide, 20 cm tall and 5 cm thick, and they kept perfect time, i.e. they each ticked
exactly once per second. As they approach you they are oriented such that their 10
cm width is aligned in the same direction as their velocities. A) (10 pts) According to your measurements how much time passes between two ticks of the clock approaching from your right and how much time passes between two
ticks of the clock approaching from your left?
The “proper time” between the events consisting of two consecutive ticks of either
of the two clocks is exactly 1 second. You measure a longer time by a factor of
”y = 1.67, i.e. a longer time interval passes in your frame than in the rest frame
of either of the clocks. You measure a time of 1.67 seconds between the ticks of
either clock. It does not matter whether the clock is going to the right or to the
left. B) (10 pts) If you measure the width, height and thickness of each of the clocks what -
are the dimensions of the clock approaching from your right and what are the
dimensions of the clock approaching from your left? .The widths are measured to be WCLOCKS = WLAB/fy = 6.0 cm. The heights and thicknesses are unchanged. H = 20 cm, T = 5 cm.-
It does not matter Whether the clocks are going to the right or to the left. ...
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