Download PHYS 1112 In-Class Exam #1B Thu. Feb. 5, 2009, 2:00pm-3:15pm

Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
PHYS 1112 In-Class Exam #1B
Thu. Feb. 5, 2009, 2:00pm-3:15pm
This is a closed-book, closed-notes exam. The last exam pages are sheets of formulae and
numerical data for you to consult.
The exam consists of 12 multiple-choice questions. Each question is worth one raw score
point. There will be no penalty for wrong answers. No partial credit will be given. I
recommend that you read all the questions at the start so that you can allocate your time
wisely. (Answer the easy questions first!)
You may use a scientific calculator for arithmetic only; your calculator must be non-graphing,
non-programmable, and non-algebraic. You are not allowed to share your calculator. The
use of cell phones, pagers, PDAs, or any other electronic devices (besides calculators) is
forbidden. All such gadgets must be turned off and put away; distractions caused by these
devices will not be tolerated.
• Do not open the exam until you are told to begin.
• Make sure the scantron sheet has your name and your UGA Card ID (810-...) number
filled in. Make sure you also have entered your name, UGA Card ID number and
signature on the exam cover page (this page!) below.
• At the end of the exam period you must hand in both your scantron sheet and the
exam paper, with the cover page signed and your name and UGA Card ID (810-...)
number filled-in. You are not permitted to take your, or any other, copy of the exam
paper out of the classroom.
• Your exam will not be graded, and you will receive a score of zero, if you do not hand
in both a properly filled in scantron sheet and the exam paper with properly filled-in
and signed cover page.
• You have until the end of the class period (i.e. until 12:15pm for Period 3 Class, until
3:15pm for Period 5 Class) to finish the exam and hand in the required exam materials
described above.
By signing below, you indicate that you understand the instructions for this exam and agree
to abide by them. You also certify that you will personally uphold the university standards
of academic honesty for this exam, and will not tolerate any violations of these standards by
others. Unsigned exams will not be graded.
Name (please print):
UGACard ID (810-...) #:
Signature:
1
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Conceptual Problems
Problem 1: An observer O, facing a mirror, observes a light source S, with the observer,
source and mirror positioned as shown here:
!"##$#
!
1
3
"
4
2
Where does O perceive the mirror image of S to be located ?
(A)
(B)
(C)
(D)
(E)
Position 1.
Position 2.
Position 3.
Position 4.
The image of S cannot be seen by O in the configuration shown above.
Problem 2: Sound waves (including ultrasound) have a speed of wave propagation vAir =
346m/s in air and vWater = 1497m/s in water. Also, note that sin(13.364o) = 346/1497 .
A narrow ultrasound beam striking the flat water surface of your swimming pool
(A) will undergo total internal reflection if incident from below the water surface for
any angle of incidence greater than 13.364o;
(B) will undergo total internal reflection if incident from above the water surface with
an angle of incidence of 8.5o ;
(C) will undergo total internal reflection if incident from below the water surface with
an angle of incidence of 8.5o ;
(D) will have an angle of refraction smaller than the angle of incidence if the beam is
incident from below the water surface;
(E) will have an angle of refraction greater than the angle of incidence if the beam is
incident from below the water surface.
2
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Problem 3: If a real object is placed more than two focal lengths away from a concave
mirror(f > 0), then the image is
(A)
(B)
(C)
(D)
(E)
virtual, erect and enlarged in height relative to the object
virtual, erect and reduced in height relative to the object
real, inverted and reduced in height relative to the object
real, inverted and enlarged in height relative to the object
real, erect and reduced in height relative to the object
Problem 4: Two non-parallel light rays initially converge to a single point on a flat screen
so that the normal to the screen is enclosed between the two incident rays, as shown here:
A slab of glass is now placed somewhere in front of the screen, in the path of the light
rays, so that the slab’s two planar glass surfaces are parallel to the screen. The index of
refraction (IoR) of the glass is greater than the IoR of the surrounding air. Where is the
new convergence point of the rays?
(A)
(B)
(C)
(D)
(E)
On the screen (unchanged);
Toward the glass slab, in front of the screen (i.e., between slab and screen);
Further away from the glass slab, behind the screen;
Inside the glass slab;
Any of the above [(A), (B), (C) or (D)] are possible, depending on the angles of
incidence of the two rays.
3
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Numerical Problems
Problem 5: A beam of monochromatic light with a frequency of 3.571 × 1014 Hz in air
travels from air into water, with indices of refraction nAir = 1.00 and nWater = 4/3, in air
and water, respectively. To an under-water observer, the light beam while traveling in water
will
(A) have a wavelength of 840nm, have the same frequency as in air, and be invisible
the human eye;
(B) have a wavelength of 630nm, have the same frequency as in air, and be invisible
the human eye;
(C) have a wavelength of 840nm, have a frequency of 4.761 × 1014 Hz, and be invisible
the human eye;
(D) have a wavelength of 840nm, have a frequency of 4.761 × 1014 Hz, and be visible
the human eye.
(E) have a wavelength of 630nm, have a frequency of 4.761 × 1014 Hz, and be visible
the human eye;
to
to
to
to
to
Problem 6: The state highway patrol radar guns send out a frequency of 9.34 GHz. You’re
approaching a radar speed trap and the radar gun detects the frequency of the radar wave
reflecting from your car. The reflected frequency is measured to be 6.98 × 10−6 % larger than
the original frequency sent out by the radar gun. Does this percentage of frequency change
depend on the frequency sent out by the radar gun ? How fast were you driving ?
(A)
(B)
(C)
(D)
(E)
driving
driving
driving
driving
driving
20.94m/s, percentage does not depend on frequency;
10.47m/s, percentage does depend on frequency;
10.47m/s, percentage does not depend on frequency;
5.24m/s, percentage does depend on frequency;
5.24m/s, percentage does not depend on frequency.
Problem 7: A flat circular mirror of radius 0.190m lies flat on the floor. Centered above
the mirror at a height of 0.590m is a light source. The circular spot formed on the ceiling by
the reflection of the light has a diameter of 2.20m. How high is the ceiling, measured from
the floor ?
(A)
(B)
(C)
(D)
(E)
1.41m
2.83m
3.00m
5.65m
6.00m
4
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Problem 8: In flint glass, red light has an index of refraction (IoR) nR = 1.765 and violet
light has an IoR nV = 1.796, while both have an IoR nAir = 1.000 in air. A beam of white
light enters a triangular prism of flint glass from air at normal incidence at the front surface
and then stikes the prism’s back surface at an angle of incidence φ = 25.0o as shown here:
!
!"#
$%&'"(
The prism is surrounded by air. What is the angle of divergence, enclosed between the red
and the violet beam after leaving the prism through the back surface ?
(A)
(B)
(C)
(D)
(E)
0.122o
0.244o
0.488o
1.140o
2.073o
Problem 9: A candle placed 40.00cm to the left of a curved mirror produces an image
60.00cm to the left of the mirror. What is the spherical radius of the mirror and where is
the center C of that sphere ?
(A)
(B)
(C)
(D)
(E)
−24.00cm, C to the left of the mirror;
+24.00cm, C to the left of the mirror;
−48.00cm, C to the right of the mirror;
+48.00cm, C to the left of the mirror;
Cannot be determined from infomation given.
5
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Problem 10: If the candle in Problem 9 is 15.0cm tall its image produced by the mirror
will be
(A)
(B)
(C)
(D)
(E)
real, inverted and 10.0cm tall;
virtual, erect and 10.0cm tall;
virtual, inverted and 22.5cm tall;
virtual, erect and 22.5cm tall;
real, inverted and 22.5cm tall.
Problem 11: A convergent lens (no.1), placed to the right of a small gem stone produces an
image of the gem 22.65cm to the right of lens no.1. If a divergent lens (no.2) of focal length
f2 = −6.42cm is now placed somewhere to the right of lens no.1, the final image produced
by lens no.2 appears approximately 35.0cm to the right of lens no.2. Approximately, how
far apart are the two lenses ? Is the object of lens no. 2 virtual or real ?
(A)
(B)
(C)
(D)
(E)
lenses
lenses
lenses
lenses
lenses
are
are
are
are
are
17.2cm
17.2cm
14.8cm
14.8cm
57.7cm
apart,
apart,
apart,
apart,
apart,
lens
lens
lens
lens
lens
no.2
no.2
no.2
no.2
no.2
object
object
object
object
object
is
is
is
is
is
real
virtual
real
virtual
real
Problem 12: A telescope produces a final image of a skyscraper (as seen through the
eyepiece) which appears to be 3.6cm tall and located 40.0cm from the eyepiece on the
incoming side of the eyepiece lens. Assume the skyscraper is at a distance of 20km; and the
telescope has achieved a 9.0-fold angular magnification, compared to viewing the building
from the actual 20.0km distance without instrument. What is the approximate height of the
actual skyscraper ?
(A)
(B)
(C)
(D)
(E)
500m
450m
400m
300m
200m
6
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Formula Sheet
Wave Propagation and Wave Nature of Light
Periodic Wave Condition:
v = λf =
λ
τ
Index of Refraction (IoR) for electromagnetic waves, definition:
n=
Doppler Effect:
c
v
!
f" = f 1 ±
u"
v
Reflection and Refraction of a Single Ray
For angle of incidence (Θ1 ), angle of reflection (Θ̄1 ) and angle of refraction (Θ2 ):
Archimedes’ Law of Reflection:
Θ1 = Θ̄1
Snell’s Law of Refraction:
sin(Θ1 )/v1 = sin(Θ2 )/v2
where v1 and v2 are the speeds of wave propagation in the respective media. For electromagnetic waves, this is also written as
Snell’s Law in IoR Form:
n1 sin(Θ1 ) = n2 sin(Θ2 )
where n1 ≡ c/v1 and n2 ≡ c/v2 are the corresponding IoR.
7
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Image Formation and Optical Instruments
Image-Object-Relations for a Single Device (Lens or Mirror):
Mirror / Thin Lens Equations:
1
1
1
+ " =
d d
f
m≡
,
h"
d"
=−
h
d
where d = object distance, d" = image distance, h = object height, h" = image height, f =
focal length, m = lateral magnification.
Focal length for reflection at a curved surface (mirror):
f = R/2
Sign Conventions for Single Device (Lens or Mirror):
d > 0 (real object) if object on ”incoming” side; else d < 0 (virtual object).
d" > 0 (real image) if image on ”outgoing” side; else d" < 0 (virtual image).
If m > 0 then image erect (upright) rel. to object; else, if m < 0 then image inverted
(upside-down) rel. to object.
If f > 0 then F on ”incoming” and F " on ”outgoing” side; else, if f < 0 then F not
on ”incoming” and F " not on ”outgoing” side.
R > 0 if center of spherical surface on ”outgoing” side; else R < 0. (For reflection at a
curved surface only.)
Compound Instrument:
If image by device 1 serves as object for device 2 and L =separation of devices then
d"1 + d2 = L,
h2 = h"1 ,
m12 = m1 × m2 ,
where m12 is total lateral magnification of image by 2 relative to object of 1.
Angular Magnification:
Definition:
|M| = Θe /Θref
where Θe =angle subtended at eye by optical instrument’s final image; and Θref =reference
angle subtended at eye by original object viewed without optical instrument at reference
distance dref
8
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Algebra and Trigonometry
2
az + bz + c = 0
sin θ =
opp
,
hyp
⇒
cos θ =
z=
adj
,
hyp
−b ±
√
b2 − 4ac
2a
tan θ =
opp
sin θ
=
adj
cos θ
sin2 θ + cos2 θ = 1
For very small angles θ (with |θ| & 90o):
sin θ ∼
= θ (in radians)
= tan θ ∼
Numerical Data
Speed of light in vacuum:
c = 3.00 × 108 m/s
Range of vacuum wavelengths visible to the human eye: from 700nm to 400nm.
Index of refraction of
vacuum: nV = 1.0 (exact).
air: nAir ∼
= 1.0.
water: nWater ∼
= 4/3 ∼
= 1.33.
Other numerical inputs (IoR, angles, lengths, etc.) will be provided with each problem
statement.
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