HW2Problem_Set2_2023
docx
keyboard_arrow_up
School
University of South Florida *
*We aren’t endorsed by this school
Course
4931
Subject
Mechanical Engineering
Date
Feb 20, 2024
Type
docx
Pages
7
Uploaded by BaronTurtleMaster4039
Audrey Gabbard
BME 6931
Problem Set 2 – Due Friday September 15, 2023 at 5:00 PM EST
Total 150 points
1. (50 points) – Set up a Michelson interferometer to measure the wavelength of a light
beam, and also to measure the index of refraction (n) of a substance. Refer to the
accompanying diagram. The light source (a tunable laser) at left shines light onto a
beam splitter. The split beams each hit a mirror (M1, M2), one of which is movable (M2),
then recombine at the beam splitter and continue to a detector for light intensity. You
will write Matlab code to detect the intensity
of the recombined beam as a function of
the position of M2. A. Assume that both M1 and M2 are initially set to be 10 cm from the beam
splitter. Move M2 away from the beam splitter in 0.025 µm increments over a
distance of 2µm. At each position of M2 (including the 10cm initial position),
compute the resultant intensity of light at the detecto
r. Repeat the
calculation for wavelengths of light between 350 and 800 nm, in 50 nm
increments.
a. Plot your intensity data for each wavelength separately, in a 5 row X 2
column array (10 different wavelengths). Keep the scales for the abscissa
and ordinate identical across plots.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 350nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 400nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 450nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 500nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 550nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 600nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 650nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 700nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 750nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 800nm
Intensity Plots at each Wavelength on M2"s distance from beam splitter
b. For each wavelength, indicate the distance that the mirror was moved
between two maxima in your plots. Then use that value to calculate the
wavelength of the light
, which should match the wavelength that you
introduced into the interferometer and quantified by moving M2.
c. In words, indicate what measurement is most fundamental for your
calculations, and which also determines the accuracy of the
interferometer.
The most important measurement for the calculations is ……………………………………..
Something with the lens?????
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 350nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 400nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 450nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 500nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 550nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 600nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 650nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 700nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 750nm
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Distance (um)
0
0.5
1
Intensity (W/m
2
)
Intensity at 800nm
Intensity Plots at each Wavelength on M2"s distance from beam splitter
X 0.7
Y 1
X 1.4
Y 1
X 0.7
Y 1
X 0.35
Y 1
X 0.9
Y 1
X 0.45
Y 1
X 0.8
Y 1
X 0.4
Y 1
X 1
Y 1
X 0.5
Y 1
X 1.1
Y 1
X 0.55
Y 1
X 1.3
Y 1
X 0.65
Y 1
X 1.5
Y 1
X 0.75
Y 1
X 1.2
Y 1
X 0.6
Y 1
X 1.6
Y 1
X 0.8
Y 1
B. Some guidance for computing intensity: a)
You’ll need to calculate the phase shift between the light paths that was
introduced by moving M2. b)
Next, calculate the sum of two sine waves with that phase shift. a.
Sample the sine waves at 0.1*π increments through one complete
cycle (2π) and add the values at each sample point. c)
To compute intensity, square each value of the summed sine wave (recall
Intensity is proportional to Amplitude
2
). d)
Sum the 21 values and divide by 21 to achieve the average intensity.
2. (30 points) Using the interferometer from problem 1, we will measure the index of
refraction (n) of a thin piece of glass.
A. Introduce into the middle of the light path from the beam splitter to M1 (at the 5
cm location) a piece of glass 1mm thick. For the purpose of this problem, assume
that the glass has index of refraction n = 1.4.
a. For lambda = 500 nm, plot the intensity profile while moving M2 as in
problem 1 without and with the piece of glass introduced into the light
path. Plot both profiles on the same graph.
M1 is 5cm from beam splitter
Thickness of glass, h = 1mm
Index of refraction of glass, n = 1.4
Lambda = 500nm
Plot intensity vs distance twice without glass and then with glass in light path on same
graph
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Huygen’s interpretation of light refraction. Draw your own diagram, with equally space radiating centers at the surface of the glass, to explain the angle of refraction.
b. If you received the data that you plotted, knowing only the thickness of
the piece of glass, how would you use the information to calculate n?
Write Matlab code to generate your plots and comment on your thought
process for each step.
Imagine not knowing n (index of refraction), inference from the two plots with and
without the glass, then go backwards to prove the calculation of n
3. (20 points) Using the wavelet approach of Huygens, and the attached diagram,
describe how the plane wave incident in air at 60° from vertical to a flat piece of glass is
refracted in its direction through the glass. The diagram is from lecture, and the incident
plane wave in the diagram is not 60° to the surface of the glass, so you’ll need to draw
your own diagram, based on the diagram pictured here.
Draw on paper the excitation of each atomic center at each step of time as a
radiating circle, with the circle diameters in the glass as 2/3 the diameter of the
circles outside of the glass.
Draw a straight line across the fronts of each set of wavelets at each point in time
Measure the refraction angle on your drawing with a compass and report the
actual value.
Does your measured angle and refractive index values approximately follow
Snell’s Law? Show your work.
4. (5 points) From the ppt of Week 3, Lecture 2, slide 8, perform the last algebraic steps
[Substitute (13) into (10)…] and arrive at equation 14. Show clearly each step of your
work.
INSERT PICTURE OF WORK DONE ON PAPER
Is equation 14 correct?
o
Yes!
One important check in a physics problem is to determine if the units cancel and
are correct. Equation 14 should have the units of coulomb (C) for charge (Q).
Show clearly each step of your work.
Q
=
18
π
d
∗
g
V
∗
√
η
3
v
f
3
2
ρg
∗(
1
+
v
r
v
f
)
Q is charge o
Units: Coulomb or FIND CONVERSION
……………………………………
d is distance
o
Units: meters
g is gravity, 9.81m/s^2
o
Units: m/s^2
V is voltage
o
Units: Volts
η is viscosity (of air)
o
Units: Pa*s or kg/(m*s)
ρ is rho (of oil)
o
Units: kg/m^3
v
f
is falling velocity
o
Units: m/s
v
r
is rising velocity
o
Units: m/s
5. (20 points) Calculate the velocity of electrons moving through the column of an electron microscope
. a.
From the example equation in the lecture relating 100,000 eV of kinetic energy to particle velocity (100 keV = (1/2)mv
2
, and the deBroglie relation l = h/mv, generate an expression relating v to l. Symbols are: e = electron charge, m = electron mass, c = speed of light, h = Planck’s constant. Show your work.
Momentum p = mv (I think)
Lambda = h/mv = h/p
b.
Write a Matlab script, to calculate velocities and wavelengths when electrons are accelerated by the high voltage transmission electron microscope (TEM) (1MeV),
intermediate voltage TEMs (400keV, 200keV), standard voltage TEM (100keV), 30keV typical of an SEM, an SEM adjusted for a landing voltage of 2.5keV and 1keV, and 200V more typical of a cathode ray tube.
c.
Plot wavelength(lambda) and velocity vs these electron energies, using the left y-
axis for wavelength and a second y-axis plotted at the right side of the graph for velocity.
d.
Comment on the values you plotted, and indicate if you think there are problems with any of the values.
e.
Research the fastest serve recorded in men’s tennis.
World’s Fastest Men’s & Women’s Tennis Serves Ever Recorded (tenniscompanion.org)
a.
Using typical metrics for a tennis ball, calculate the associated wavelength
of the tennis ball during the serve. Wavelength,l ambda during serve
=
¿
b.
Calculate the wavelength for a baseball traveling at the same speed.
Wavelength,lambdabaseball
=
¿
c.
Comment on the different values.
i.
The difference in the tennis ball and baseball involve 6. (10 points) Compare a TEM to a SEM.
a.
Draw the elements of the electron optical train for transmission (TEM) and scanning (SEM) electron microscopes.
b.
List the elements of the TEM that could be used in construction of a SEM without modification. c.
List and indicate the functions of the elements that are found only in the SEM.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
d.
For these SEM elements, indicate why they are placed where they are placed.
e.
What electron detector types are used in SEM? Research and report on the energy range of electrons captured using each detector.
7. (20 points) Re-visit the layer 2 pyramidal cell Narration, and inspect carefully the
spines on the dendrites.
If you were permitted to generate up to 6 classes of spines from qualitative
expression, what would they be? Feel free to choose fewer than 6 categories.
Draw your examples, and in no more than a few bullet points, define their
features. Draw examples of spines that are most difficult to categorize.
Trace along the main apical dendrite (straightest route to the brain surface).
Approximately divide the length into 4 equal segments. Record the number of
each of your types of spines in each of the 4 segments.
Send your spreadsheet of values. Comment on any observations or conclusions
you draw from your data.
Related Documents
Related Questions
Don't Use Chat GPT Will Upvote And Give Handwritten Solution Please
arrow_forward
Don't Use Chat GPT Will Upvote And Give Handwritten Solution Please
arrow_forward
Given the following scene on the stage
Player #1
Player #3
Diameter 1meter
Diameter 2meters
Player #2
High 2m
Width 1m
All spotlights are place at 15 meters from the stage. You want to
produce a circle of light of 2meters diameter with the
SPOTLIGHT#1 on the Player #1, a rectangle of light of 2m by
Im with the SPOTLIGHT #2 on the Player #2 and a circle of
light of Imeter diameter with the SPOTLIGHT#3 on the Player
#3
arrow_forward
What is the Wave Machine?
The below animation and diagram show a wave machine at Stonybrook University in New York. Use your observation of the animation and the labeled diagram below to help you answer the questions that follow:
Image Attached
The first wave measures 2 inches from the gray line to the top of the red line. If a larger second wave measured 4 inches from the gray line to the top of the red, then each wave would have two times more energy than the first wave.
(a) 16 times
(b) 4 times
(c) 8 times
arrow_forward
how do I dimension the object shown below
assume grid spacing is 0.2
arrow_forward
3¹
TE
MY NOTES
ASK YOUR TEACHER
SAMC)
If the RR Lyrae stars in a globular cluster have average apparent magnitudes of +16, how far away (in pc) is the cluster? (Hints: See the following figure, and use the magnitude-distance
formula: d = 10(my-Mv+5)/5.)
Absolute magnitude
pc
6
0
0.3
Type I
(classical)
Cepheids
Type II
Cepheids
RR Lyrae stars
10
Pulsation period (days)
30
104
103
10²
100
Luminosity, L/L
Ⓡ
arrow_forward
You are watching a live concert. You can also find the concert streaming live on Spotify. About how far must you stand from the stage in order for
the live concert and the live stream to be perfectly in sync?
HINT: Assume the radio signal (Spotify) has to travel all the way around the Earth.
circumference of the Earth (average): 40,041,000 m
Speed of sound: 345 m/s
Speed of light: 300,000,000 m/s
arrow_forward
Send handwritten solution
arrow_forward
Engineering Drawing TS: True Size EV: Edge ViewTrue or False 1. It is possible that a plane will appear in TS in two consecutive reference planes.
2. It is possible that a plane will appear in EV in two consecutive reference planes.
3. Is it possible to show two planes in TS in a single reference plane.
4.
arrow_forward
Red light is incident in air on a 30° -60° - 90 ° prism as shown. The incident beam is directed at an angle of ₁ = 47.9⁰
with respect to the horizontal and enters the prism at a height h = 27 cm above the base. The beam leaves the prism to
the air at a distance d = 67.5 along the base as shown.
52.2
30⁰
1.596
1) What is 2, the angle the beam in the prism makes with the horizontal axis?
01
d
degrees Submit
2) What is n, the index of refraction of the prism for red light?
12.34485142
Your submissions: 52.2 ✓
Computed value: 52.2
Submitted: Tuesday, November 15 at 11:03 AM
Feedback: Your answer has been judged correct; the exact answer is: 52.4776287536106.
Submit
|h
$3
Your submissions: 1.596
Computed value: 1.596
Submitted: Tuesday, November 15 at 11:03 AM
Feedback: Your answer has been judged correct; the exact answer is: 1.60120151624339.
Your submissions: 12.34485142 X
3) What is 3, the angle the transmitted beam makes with the horizontal axis?
degrees Submit
G
arrow_forward
EXERCISE 03
DATE:
115
GIVEN THE ORTHOGRAPHIC VIEWWS, CREATE AN ISOMETRIC SKETCH OF THE FOLLOWING OBJECT.
VISUALIZATION 6 ENGINEERING DESIGN GRAPHICS WITH AUGMENTED REALITY
arrow_forward
Answer CORRESPONDING to what is given in the image. The instruction is already on the image given below. Thank you
arrow_forward
AutoSave
STATICS - Protected View• Saved to this PC -
O Search (Alt+Q)
Off
ERIKA JOY DAILEG
EJ
File
Home
Insert
Draw
Design
Layout
References
Mailings
Review
View
Help
Acrobat
O Comments
E Share
PROTECTED VIEW Be careful-files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View.
Enable Editing
Situation 9 - A 6-m long ladder weighing 600 N is shown in the Figure. It is required to determine
the horizontal for P that must be exerted at point C to prevent the ladder from sliding. The
coefficient of friction between the ladder and the surface at A and B is 0.20.
25. Determine the reaction at A.
26. Determine the reaction at B.
27. Determine the required force P.
4.5 m
1.5 m
H=0.2
30°
Page 5 of 5
671 words
D. Focus
100%
C
ЕPIC
GAMES
ENG
7:24 pm
w
US
16/02/2022
IZ
arrow_forward
Dr. Ammar T. Al-Sayegh
Problem: 5
Name:
The positions of point A
on the building and point
B on the antenna have
been measured relative to
the electronic distance
meter (EDM) at O.
Determine the distance
between A and B. (Hint:
Formulate a position
vector directed from A to
B; then determine its
magnitude.)
Page 8
B
60
653 m
55%
ID:
460 m
40°
30
ENG202 - Statics
arrow_forward
77. Asketch of a manufactured part is given below the drawing. Sketch the planes of a datum reference
frame in all of the views of the manufactured part. Label each of the datum planes that make up the
datum reference frame and note the number of points of contact required with the feature surface.
Complete the sketch based on a feature control frame that references datum feature A primary,
B secondary, and C tertiary.
스028시
HB
Drawing
Manufactured part
arrow_forward
AB is a straight line, the coordinates
of its ends are as follows: A= (1, 2), B=
(5, 4) right of A. Distance between
projectors =7 cm.The horizontal trace
H= (-2, 0) left of ARequired:Draw
(scale 1:1) the ELEVATION and PLAN
of the line and find the following:(1)
Its true length.(2) The coordinate of
its traces.(3) Its inclination of the H.P
and V.P.(4) Check the value of H given
* .in the question is it True or False
arrow_forward
how do I dimension the object shown below
assume grid spacing is 0.2
arrow_forward
LESSON: AUTODESK FUSION 360
Choose from the choices below:
arrow_forward
3) If two forces of 10,000 N are continuously rotating 1,000,000 shafts, the ball bearings and shaft
thickness must be selected. The system should be drawn in 3D and proven to work safely. Please
note that you must determine the dimensions of the system and the shaft material and code
yourself. This question should only be answered if you are between 61 and 90 in the student list
(#61-90).
F
Bearing
☑ ☑
☑ ☑
Shaft
F
arrow_forward
1. Use the collision theory to explain why a lump of sugar is better to use in hot cup of tea ,but granulated sugar is better to use in iced tea.
2.suppose you held a lighted match to a solid pieces of wood and another match to a pile of wood shavings .which form of wood catch fire more easily and why?
arrow_forward
System for shorter flight times With his invention, Håkan Lans has made it possible to shorten flight times. Thanks to his invention, a pilot can see the exact positions of other aircraft. ( what is the right answer?
Registered design
Logo
Patent
d. Copyright
arrow_forward
SEE MORE QUESTIONS
Recommended textbooks for you
Precision Machining Technology (MindTap Course Li...
Mechanical Engineering
ISBN:9781285444543
Author:Peter J. Hoffman, Eric S. Hopewell, Brian Janes
Publisher:Cengage Learning
Related Questions
- Don't Use Chat GPT Will Upvote And Give Handwritten Solution Pleasearrow_forwardDon't Use Chat GPT Will Upvote And Give Handwritten Solution Pleasearrow_forwardGiven the following scene on the stage Player #1 Player #3 Diameter 1meter Diameter 2meters Player #2 High 2m Width 1m All spotlights are place at 15 meters from the stage. You want to produce a circle of light of 2meters diameter with the SPOTLIGHT#1 on the Player #1, a rectangle of light of 2m by Im with the SPOTLIGHT #2 on the Player #2 and a circle of light of Imeter diameter with the SPOTLIGHT#3 on the Player #3arrow_forward
- What is the Wave Machine? The below animation and diagram show a wave machine at Stonybrook University in New York. Use your observation of the animation and the labeled diagram below to help you answer the questions that follow: Image Attached The first wave measures 2 inches from the gray line to the top of the red line. If a larger second wave measured 4 inches from the gray line to the top of the red, then each wave would have two times more energy than the first wave. (a) 16 times (b) 4 times (c) 8 timesarrow_forwardhow do I dimension the object shown below assume grid spacing is 0.2arrow_forward3¹ TE MY NOTES ASK YOUR TEACHER SAMC) If the RR Lyrae stars in a globular cluster have average apparent magnitudes of +16, how far away (in pc) is the cluster? (Hints: See the following figure, and use the magnitude-distance formula: d = 10(my-Mv+5)/5.) Absolute magnitude pc 6 0 0.3 Type I (classical) Cepheids Type II Cepheids RR Lyrae stars 10 Pulsation period (days) 30 104 103 10² 100 Luminosity, L/L Ⓡarrow_forward
- You are watching a live concert. You can also find the concert streaming live on Spotify. About how far must you stand from the stage in order for the live concert and the live stream to be perfectly in sync? HINT: Assume the radio signal (Spotify) has to travel all the way around the Earth. circumference of the Earth (average): 40,041,000 m Speed of sound: 345 m/s Speed of light: 300,000,000 m/sarrow_forwardSend handwritten solutionarrow_forwardEngineering Drawing TS: True Size EV: Edge ViewTrue or False 1. It is possible that a plane will appear in TS in two consecutive reference planes. 2. It is possible that a plane will appear in EV in two consecutive reference planes. 3. Is it possible to show two planes in TS in a single reference plane. 4.arrow_forward
- Red light is incident in air on a 30° -60° - 90 ° prism as shown. The incident beam is directed at an angle of ₁ = 47.9⁰ with respect to the horizontal and enters the prism at a height h = 27 cm above the base. The beam leaves the prism to the air at a distance d = 67.5 along the base as shown. 52.2 30⁰ 1.596 1) What is 2, the angle the beam in the prism makes with the horizontal axis? 01 d degrees Submit 2) What is n, the index of refraction of the prism for red light? 12.34485142 Your submissions: 52.2 ✓ Computed value: 52.2 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 52.4776287536106. Submit |h $3 Your submissions: 1.596 Computed value: 1.596 Submitted: Tuesday, November 15 at 11:03 AM Feedback: Your answer has been judged correct; the exact answer is: 1.60120151624339. Your submissions: 12.34485142 X 3) What is 3, the angle the transmitted beam makes with the horizontal axis? degrees Submit Garrow_forwardEXERCISE 03 DATE: 115 GIVEN THE ORTHOGRAPHIC VIEWWS, CREATE AN ISOMETRIC SKETCH OF THE FOLLOWING OBJECT. VISUALIZATION 6 ENGINEERING DESIGN GRAPHICS WITH AUGMENTED REALITYarrow_forwardAnswer CORRESPONDING to what is given in the image. The instruction is already on the image given below. Thank youarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Precision Machining Technology (MindTap Course Li...Mechanical EngineeringISBN:9781285444543Author:Peter J. Hoffman, Eric S. Hopewell, Brian JanesPublisher:Cengage Learning
Precision Machining Technology (MindTap Course Li...
Mechanical Engineering
ISBN:9781285444543
Author:Peter J. Hoffman, Eric S. Hopewell, Brian Janes
Publisher:Cengage Learning