Physics 215 – Fall 2006
Name: ______________________
Homework Journal #14:
Wave Optics
Instructor: ___________________
Section:
Date Due: M34/T34
M1 M2 M3 M4 M5 M6
T1 T2 T3 T4 T5 T6
INSTRUCTIONS: To receive full credit, you must fully justify your answers and show all written
work (including algebraic steps) in a neat and orderly fashion. If your work is disorganized or the
grader cannot follow you logic, you will be penalized. Avoid writing down single answer solutions –
the homework problems, like the GRs, are generally designed to require multiple steps and, with only a
few exceptions, are not “plug and chug” exercises.
AUTHORIZED RESOURCES: Please document any instructor(s) and/or student(s) you consulted
and the precise nature of the assistance you received in completing this assignment. You DO NOT
need to document use of the text, class handouts, or your own classroom instructor. Any published or
unpublished material, or internet source, does not need to be documented unless the material
specifically aims at answering problems in Mastering Physics.
DOCUMENTATION:
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Problem Name
Points
Possible
Points
Earned
Problem Name
FM Radio Interference
Path Length
Difference
Interference of Two
Radio Waves
The First Dark Fringe
Single-Slit Diffraction
Problem 22.30
AM Radio in a City
Total:
_______ / 32
1/10
Points
Possible
Points
Earned
Problem Name: FM Radio Interference
Description: You are listening to the FM radio in your car. As
you come to a stop at a traffic light, you notice that the radio signal is
fuzzy. By pulling up a short distance, you can make the
reception clear again.
Assume that the transmitter is very far away, and that the building is
at a 45-degree angle from the path to the transmitter.
Point A in the figure to the right is where you originally stopped, and
point B is where the station is completely clear again. Finally, assume
that the signal is at its worst at point A, and at its clearest at point B.
Part A: What is the distance d between points A and B? (Answer in terms of wavelengths)
Answer:
Part B: Your FM station has a frequency of _______ megahertz. The speed of light is about 3x108
meters per second. What is the distance d between points A and B?
Answer:
Physics 215 – Fall 2006
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Problem Name: Interference of Two Radio Waves
Description: Two coherent sources of radio waves, A and B, are _____ meters apart. Each source
emits waves with wavelength _____ meters. Consider points along the line connecting the two sources.
Part A: At what distance from source A is there constructive interference between points A and B?
Answer:
Part B: At what distances from source A is there destructive interference between points A and B?
Note: There will be two separate interference fringes between point A and point B.
Answer:
Answer:
Physics 215 – Fall 2006
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Problem Name: Single-Slit Diffraction
Description: You have been asked to measure the width of a
slit in a piece of paper. You mount the paper ______ cm from a
screen and illuminate it from behind with laser light of
wavelength ______ nm (in air). You mark two of the intensity
minima as shown in the figure, and measure the distance
between them to be ______ mm.
Part A: What is the width of the slit?
Answer:
Part C: Below is another interference pattern produced by single-slit diffraction.
It's hard to tell on many computer screens, but the first minima really occur at 7.5 divisions either side
of the center (it may look like it's in a different place when you print it). Each division of this scale
represents 0.01 radians; the width of the slit is ______ um.
Answer:
Physics 215 – Fall 2006
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Problem Name: Why You Can Still Receive AM Radio in a City
Description: When radio waves try to pass through a city, they encounter thin vertical slits: the
separations between the buildings. This causes the radio waves to diffract. In this problem, you will see
how different wavelengths refract as they pass through a city and relate this to reception for radios and
cell phones. You will use the angle from the center of the central intensity maximum to the first
intensity minimum as a measure of the width of the central maximum (where nearly all of the
diffracted energy is found).
Consider radio waves of wavelength λ entering a city where the buildings have an average separation
of a.
Part A: Find the angle θ to the first minimum from the center of the central maximum.
Assume that the average spacing between buildings is a = 20 meters.
Answer:
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Homework Journal #14
Part B: What is the angle θ to the first minimum for an FM radio station with a frequency of _____
MHz?
Answer:
Part C: What is the angle for a cellular phone that uses radio waves with a frequency of _____ MHz?
Answer:
Physics 215 – Fall 2006
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Problem Name: Path Length Difference
Description: A third order maxima in a double slit experiment (slits spaced _____ mm apart, slit to
screen distance is _____ m) is found _____ cm away from the central maxima.
The wavelength of light used in the experiment is 600nm.
Part A: What is the path length difference between the two light rays that formed the third order
fringe?
Answer:
Physics 215 – Fall 2006
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Problem Name: Double Slit 2
Description: A laser with wavelength d/8 is shining light on a double slit with slit separation _____
mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to
shine a second laser, with a different wavelength, through the same slits.
Part A: What is the wavelength λ2 of the second laser that would place its second maximum at the
same location as the fourth minimum of the first laser, if d = _______ mm?
Answer:
Physics 215 – Fall 2006
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Problem Name: The First Dark Fringe...
Description: Coherent light with wavelength ______ nm passes through two very narrow slits, and
the interference pattern is observed on a screen a distance of ______ m from the slits. The first-order
bright fringe is a distance of ______ mm from the center of the central bright fringe.
Part A: For what wavelength of light will the first-order dark fringe be observed at this same point on
the screen?
Answer:
Physics 215 – Fall 2006
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Problem Name: Knight Problem 22.30
Description: A double slit is illuminated simultaneously with orange light of wavelength ______ nm
and light of an unknown wavelength. The m = ____ bright fringe of the unknown wavelength overlaps
the m = ______ bright orange fringe.
Part A: What is the unknown wavelength?
Answer:
Physics 215 – Fall 2006
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