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Unformatted text preview: Physics 4 Final, Saturday, March 22, 2008 Name: Solﬁx‘o V'LS Seat:
Exam form A Do not begin until instructed to do so. You may use a calculator and one (double—sided) page of handwritten notes. 1. (10 points) Answer the following true or false questions. . @or F) 2 X a = 3}.
. (T or®(3:ﬁ + 42) x (5:5)) = 152. o (T or The index of refraction of air is larger than the index of
refractlon of water. 0 1" F) If you place a voltage across a resistor, it will produce a magnetic ﬁeld. Y4; bamuﬁt H will Pt‘Oq‘UCe. a. Curran/Vt o {T or® Light moving in air will undergo total internal reﬂection
on a water surface it the angle of incidence is high enough. 2. (2 points) A piano—convex lens is made from a glass sphere of radius
R 10 cm by grinding away part of the Sphere as shown below.
The lens is the remainder of the Sphere} with a maximum thickness
of R — d = 2 cm. For light that then moves through the lens beginning
from the ﬂat side, what is the focal length of the lens? (a) 5 cm (b) 0.4
cm (c) 0.05 cm (d) 20 cm (e) 10 cm (f) 1 cm (g) 5 cm (h) —0.4 cm 005 cm@k) —10 cm (1) —1 cm .L __.L
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._10 M 3. (4 points) The ﬁgures below show interference patterns as intensity vs
angle. For each of the descriptions of slit arrangements listed in the left
column choose the letter of the best matching ﬁgure in the right column. i a A single slit of width 0: < A. (a.@, c, d) o A single slit of width (1 > A. (a, b, c, : A grating of two slits of width 0. < A. b. c, d) o A grating of many slits of width (1 < A.
(a, b, @d) 4. (4 points) The ﬁgure below shows two rays of light, of wavelength 600
nrn, that reflect from glass surfaces separated by 150 nm. The rays are
initially in phase. When they have cleared the reﬂection region, are the rays: exactly in phase, xactl out of phase or half way between? :lh150nm—H: T‘U “Pillar [Pad/LL M4. [hmk Plane* 5 “iii
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so mg m V M 6* PM“ 5. (15 points) A thin glass rod of length L has a charge Q uniformly
distributed over its surface. The rod is moving along the :1: axis at a
speed 1: toward the positive ac direction. Calculate the magnetic ﬁeld
produced at a point on the y axis, i.e. at (0,y, 0), for the instant in
time when one end of the rod is at the origin and the other end is at
a: = L. You must show and explain all steps, but you can stop when
you get to the point that “the rest of the calculation could be looked up fromarnath table.” Tild (5 WI. We. 7L0 Ag; ,uo Ag 31.? when Jab; L A ‘9 +11
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E1 i405” JL wadx _[ 6. (10 points) Consider a square loop of wire} with resistance R, that
lies in the :1: — y plane. It has sides of length L. Initially, a uniform
magnetic ﬁeld exists, with magnitude Bo and pointed in the 2 direction.
Beginning at a certain point in time, which we’ll call t = 0, the magnetic
ﬁeld is caused to steadily decrease such that it reaches zero within one
second. What is the EMF induced in the loop of wire at t = 0.5
seconds? 8 i3 6.. Lvuko“ 0;: 79 lapHanna. {:0 g‘ {7:}
.ﬂul' we. can. d¢$¢FCL¢ infHa B(+) : {30(1.. 4:)
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5 At; ° 7. (15 points) A toroid is made from a tightly wound solenoid that is bent
into a torus, i.e., the shape of a donut. Prove that the magnetic ﬁeld
is zero everywhere outside the toroid. You must Show and explain
all steps to get any credit. Wan!” A0 ﬂu“; Pm {100 SICd'F‘S.‘ ﬁfrﬁ' fluw ﬂu. gig
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(7'1; +FU¢ LU‘Jh/WLLLI“; Wﬁgla Mr. Jvrr‘ccir 8. (10 points) A laser is mounted as shown in the figure, a distance d from
a converging lens, which has a positive focal length of f. The laser
produces a light beam, with a wavelength of A} that travels parallel to
the optical axis of the lens at a height b, above that axis. A large screen
is placed a distance R to the right of the lens. The laser beam passes
through the lens and makes a dot on the screen at a point that is a
distance 3;, above the axis of the lens. Find 9 in terms of the variables given above.
TA‘ 7234“! '70 in f' 15 wk“; farallchl was
woulcl (31:65, 50 746“ ld—ns lawK415 714k“ 1‘9“— 9. (15 points) An object, mirror and thin lens are placed as shown below.
The focal points of the lens are indicated. Show the ray tracing that
is required to determine the ﬁnal image location, and indicate that
location. You need not calculate the position, just draw. a s
f1 3 f1 5 Final Image —> First Image —) ' '
2nd Image —> 10. (15 points) Two radio antennas are located at points A and B? a dis
tance L apart. The antennas each radiate sinusoidal radio waves at
a frequency f, but the signal transmission at antenna B is delayed in
time relative to antenna A by a quarter of a period. A radio receiver is
moved out from point B along a line perpendicular to the line connect~
ing A and B (i.e., moved along line BC shown in the ﬁgure). Determine
a distance, 11:, away from B where there will be destructive interference.
(Beware that the angles involved are not small enough to rely on small angle approximations.) _
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 Winter '08
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