Download PHYS 1112 In-Class Exam #1A Thu. Feb. 5, 2009, 11:00am-12:15pm

Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
PHYS 1112 In-Class Exam #1A
Thu. Feb. 5, 2009, 11:00am-12:15pm
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: A student runs westward at 3m/s, away from a vertical plane mirror, while
the mirror, mounted on wheels, travels eastward at 7 m/s (with both speeds given relative
to the ground). The speed at which the student’s image moves and its direction, relative to
the ground, is
(A)
(B)
(C)
(D)
(E)
4m/s westward
4m/s eastward
10m/s eastward
17m/s eastward
17m/s westward
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 have an angle of refraction smaller than the angle of incidence if the beam is
incident from above the water surface;
(B) will have an angle of refraction greater than the angle of incidence if the beam is
incident from below the water surface;
(C) cannot undergo total internal reflection if incident from above the water surface,
regardless of the angle of incidence;
(D) will undergo total internal reflection if incident from above the water surface with
an angle of incidence of 30o ;
(E) will undergo total internal reflection if incident from below the water surface with
an angle of incidence of 30o .
Problem 3: If a real object is placed between the focal point and the lens for a convergent
lens (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
2
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Problem 4: A thin lens and a curved mirror both have the same focal length when surrounded by air (with index of refraction nAir = 1). If the lens and the mirror are submerged
in water (with index of refraction nWater > 1) what happens to the focal length fL of the
lens and the focal length fM of the mirror ?
(A)
(B)
(C)
(D)
(E)
fL
fL
fL
fL
fL
changes and fM stays the same;
stays the same and fM changes;
increases and fM increases;
decreases and fM decreases;
stays the same and fM stays the same.
Numerical Problems
Problem 5: A beam of monochromatic light with a frequency of 3.75 × 1014Hz 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 800nm, have the same frequency as in air, and be invisible to
the human eye;
(B) have a wavelength of 800nm, have a frequency of 5.00 × 1014 Hz, and be visible to the
human eye;
(C) have a wavelength of 600nm, have a frequency of 5.00 × 1014 Hz, and be invisible to
the human eye;
(D) have a wavelength of 600nm, have the same frequency as in air, and be invisible to
the human eye;
(E) have a wavelength of 600nm, have a frequency of 5.00 × 1014 Hz, and be visible to the
human eye.
Problem 6: The state highway patrol radar guns send out a frequency of 9.34 GHz. You’re
approaching a radar speed trap driving 5.24 m/s and the radar gun measures the frequency
of the radar wave reflecting from your car. By what percentage is the reflected frequency
different from the original frequency ? Does this percentage change if the radar gun frequency
changes ?
(A)
(B)
(C)
(D)
(E)
1.75 × 10−6
3.49 × 10−6
3.49 × 10−6
3.52 × 10−6
3.52 × 10−6
%,
%,
%,
%,
%,
will
will
will
will
will
not change with frequency
change with frequency
not change with frequency
change with frequency
not change with frequency
3
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
Problem 7: Two plane mirrors intersect at an angle θ, as shown here:
"
#
!
A light ray is incident on one of the mirrors at an angle of α = 20o . The angle φ between
the incident and outgoing rays is 94.4o. What is θ ?
(A)
(B)
(C)
(D)
(E)
34.4o
44.4o
47.2o
54.4o
67.2o
Problem 8: In flint glass, red light has an index of refraction (IoR) nR = 1.865 and violet
light has an IoR nV = 1.896, while both have an IoR nAir = 1.000 in air. If a beam of white
light is incident from air upon a block of flint glass at an angle of incidence of 50o the angle
of divergence, enclosed between the red and the violet beam inside the glass, is
(A)
(B)
(C)
(D)
(E)
0.267o
0.344o
0.421o
1.68o
2.27o
Problem 9: A postage stamp placed 4.00cm to the left of a lens produces an image 32.0cm
to the left of the lens. What is the focal length of the lens ?
(A)
(B)
(C)
(D)
−4.57cm
+4.57cm
−3.56cm
+3.56cm
4
Physics 1112
Spring 2009
University of Georgia
Instructor: HBSchüttler
(E) Cannot be determined from infomation given.
Problem 10: If the postage stamp in Problem 9 is 1.25cm tall its image produced by the
lens will be
(A)
(B)
(C)
(D)
(E)
real, inverted and 0.156cm tall;
virtual, erect and 0.156cm tall;
virtual, inverted and 10.0cm tall;
virtual, erect and 10.0cm tall;
real, inverted and 10.0cm tall.
Problem 11: A convergent lens no.1, placed to the right of a small sand grain, produces an
image of the grain 24.7cm to the right of lens no.1. If a divergent lens no.2 of focal length
f2 = −7.42cm is now placed 18.6cm to the right of lens no.1, the final image produced by
lens no.2 appears approximately
(A)
(B)
(C)
(D)
(E)
3.35cm to the left of lens no.2
3.35cm to the right of lens no.2
34cm to the right of lens no.1
34cm to the left of lens no.2
34cm to the right of lens no.2
Problem 12: A microsope produces a final image of a bacterial cell (as seen through the
eyepiece) which appears to be 1.2cm in diameter and located 25.0cm from the eyepice on the
incoming side of the eyepiece lens. Assume the microscope has achieved a 5000-fold angular
magnification, compared to viewing the bacterium from a 25.0cm nearpoint distance without
instrument. What is the approximate diameter of the actual bacterial cell ?
(A)
(B)
(C)
(D)
(E)
24. µm
4.2 µm
2.4 µm
0.42 µm
0.24 µm
5
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.
6
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
7
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.
8