Download Keeping Your Lab Diary - University of Sheffield

University of Sheffield
Department of Physics and Astronomy
FIRST YEAR
PHYSICS LABORATORY
HANDBOOK
2007 - 2008
INTRODUCTION
Laboratory based learning is an integral part of the physics curriculum at the University of
Sheffield. You must attend the physics laboratory once per week for three hours during the
first year of your honours course. It is compulsory to separately pass the laboratory
assessment in order to pass the module as a whole. An overall laboratory assessment of 40%
is the requirement. Details of how marks are obtained are given later in this manual.
You should treat the laboratory as a learning experience. We do not expect you to have either
"all the answers" or much prior experience of laboratory work. In any first year class there is
a wide diversity of background and our aim is to accommodate that. We expect all students to
have reached an appropriate level of competence by the end of the first year, and the
supervision, activities and methods of assessment are designed to achieve this goal.
It is important that you learn and practice various experimental skills. Consequently we have
attempted to provide necessary information, but not to give you a complete recipe for you to
follow mindlessly. It has been necessary to assume some knowledge and skills when writing
the laboratory notes. If you find that you do not possess the knowledge and skills expected
you must (a) devote time to gaining the physics knowledge and (b) use the laboratory staff to
identify and learn the experimental skills required. For instance you should know that if
y∝enx then a graph of ln y versus x should yield a straight line of gradient n. If a simple power
law exists i.e. y ∝ x n then a graph of ln y versus ln x will be a straight line of gradient n.
Laboratory periods are your opportunity to put in to practice many of the concepts met in a
more abstract form elsewhere in the course. We want you to enjoy the laboratory classes, and
a team of academic staff, research workers and technicians are always available to help. On
some occasions the lack of explicit instructions on how to carry out a particular task may
cause you to feel uncertain and anxious. This is normal, confidence comes with succeeding
on your own. Do not hesitate to ask for help if you feel that you do need it.
There are a number of different activities that you will cover as the year progresses. You will
spend time on a computing course, and the other weeks in the main suite of laboratories
located on D floor of the Hicks Building. The laboratory based work is divided between basic
skill sessions, training in data handling and analysis, exercises in communicating your work
(oral and written), set-piece experiments designed to illustrate a particular point, and a
project. The detailed timetable appears elsewhere in these notes.
The class will be divided in to groups for laboratory work, and you will normally work with a
partner. The allocation to groups will take place at the laboratory session in the first week of
each semester. Some students will be working on Monday afternoons and some students
working on Thursday afternoons. The choice of afternoon may depend on the modules you
are taking. You will be assigned to a day at the registration period at the start of each
semester.
Students are expected to arrive within five minutes of the start of the laboratory class.
The laboratory is open from 1:45pm to 5pm on Monday and Thursday afternoons. At the
beginning of each session each student should check with one of the members of academic
staff what activity they will be working on and register their attendance. If you cannot attend
the laboratory for medical or personal reasons, a doctor’s certificate or other documentation
must be produced. Absences will be monitored and action taken.
1
For each experiment there is a set of notes describing what you are required to do for the
experiment and providing relevant back ground information. For the introductory
experiments the notes are included in this folder. For the later pool experiments copies of the
notes are available from the set of metal drawers in the lab. You should always aim to have
read the appropriate notes before you come to the lab session. You will get far more from the
laboratory if you take time to prepare each week
RECOMMENDED READING
Textbooks
We would highly recommend:
“Experimental methods; an introduction to the analysis and presentation of data”
Author:
L.Kirkup
Publ.
Wiley
You might also like to consult the following in the library:
“Practical physics”
Author:
G.L.Squires
Publ.
Cambridge University Press
Library:
530.72
“Scientists must write; a guide to better writing for scientists, engineers and students”
Author:
R.Barrass
Publ.
Chapman and Hall
Library:
808.06
“Statistics for technology”
Author:
C.Chatfield
Publ.
Chapman and Hall
Library:
519
(6 St Georges)
“Errors of observation and their treatment”
Author:
J.Topping
Publ.
Chapman and Hall
Library:
530.8
“A practical guide to data analysis for physical science students”
Author:
L.Lyons
Publ.
Cambridge University Press
Library:
530.72
2
SAFETY
Everyone in the laboratory should be aware of simple safety precautions. As in any building
you should know the whereabouts of fire extinguishers, blankets and escape routes. In
addition to the application of common sense there are a few simple rules:
(i)
(ii)
(iii)
(iv)
Ionising radiation - do not handle sealed radioactive sources any
more than necessary. Take care not to damage sources.
Smoking, eating and drinking in the laboratory are all
prohibited
Safety-specs should be worn when using any hot liquid (e.g. oil
baths)
Do not expose your eyes to direct laser-light
If in doubt about the safety of any procedure, check with a demonstrator or technician.
After handling laboratory equipment, you should wash your hands.
Any accident HOWEVER TRIVIAL must be reported to a demonstrator.
We must all act within the law as defined by the Health and Safety Executive and the
COSHH regulations.
STUDENT PROGRESS AND SUPPORT
One aim of laboratory teaching and training is to prepare you for the possibility of
working in a laboratory environment after graduation. Our methods of monitoring your
activity reflect how projects in industry and academe might be managed on a day to day
basis.
There are a number of people available to you during a laboratory session. The academic
staff, Prof John Cockburn and Dr Luke Wilson, are helped by a team of demonstrators drawn
from the post-graduate and post-doctoral members of the Department. Problems concerning
malfunctioning equipment and requests for equipment should be made to the laboratory
technician.
Each activity is designed to last one laboratory period. You must complete your activity,
including all calculations and graph plotting, by the end of the period allotted. No extra time
will be allocated to any given experiment. The aim of this is to encourage you to work
efficiently and to maintain a high standard of record keeping. If it is a lecture based activity
then homework will be set rather than assessed at the time.
Lab Diaries will be issued at the first teaching lab session of the year, for a nominal cost of
£1 (please remember to bring correct money to first session).
Please label the lab diary with your full name on both the spine and inside
cover.
3
Keeping Your Lab Diary
1.
What is the purpose of a lab diary?
Working scientists need to keep a detailed record of what they are doing, for a number of
reasons:
•
as a working record of an experiment in progress (for example, noting down actions
which may have a bearing on the final result, lists of items that cannot be dealt with
now, but will have to be considered later, details of the reasoning that led you to choose
one way of doing something over another which might seem just as good);
•
to ensure that good ideas or technical points are not forgotten, but can be looked up and
re-used (since the same type of problem may come up again in a different context);
•
to track down problems if things do not go according to plan (for example, if your
results do not agree with a colleague’s, your lab diary may show that you used slightly
different experimental techniques);
•
as evidence that the work was done (for example, if the award of a patent is contested
by another company).
This makes keeping a good lab diary an important part of scientific practice, and therefore
something which we should encourage you to do in your undergraduate laboratory work. In
any case, the above reasons for keeping a lab diary apply to the astronomy lab just as much as
they do to a working research lab: some assignments last more than a week, so you need a
working record; techniques such as line fitting and calculating the error on an average will
recur in different exercises; your results may not agree with the textbook, so you may need to
track down an error; and we will assess your work on the basis of the evidence provided by
your lab diary.
2.
What should your lab diary look like?
Your lab diary should be a book, not a loose-leaf folder (it is a general rule that vital items
fall out of loose-leaf folders and get lost!). A suitable lab book is provided by the
Department for a nominal cost of £1, and is issued at the first lab session of the academic
year. THIS BOOK MUST BE USED FOR ALL YOUR LAB WORK. Now that many
people do all their plotting with computers, a simple lined-paper notebook is adequate, but
additional graph paper is still useful for diagrams, plots that are difficult to make on computers or plots that are too simple to be worth writing a spreadsheet for (e.g. simple
histograms), etc.
All plots made on computer or on loose graph paper, must be fixed permanently into your
book (glue, staple or sellotape them to the appropriate page), and properly labelled.
Anonymous graphs on loose sheets will get lost, or you will forget what they refer to.
Remember that a lab diary is supposed to be a permanent record of your work (you may well
see some of your lab demonstrators referring to their lab diaries from four years ago when
they try to help you with a problem).
Since your lab diary will be used for assessment, it is important that it is legibly written and
logically laid out. It’s OK to cross things out, as long as the organisation of the material is
still clear enough for someone else to follow. It is useful to number the pages, and keep an
4
up-to-date table of contents at the front (laboratory notebooks generally provide a table of
contents page). AT THE END OF EACH SESSION YOU MUST LEAVE YOUR LAB
DIARIES ON THE BANCH. NO DIARIES ARE TO BE TAKEN FROM THE LAB.
3.
What should be in a lab diary?
Your lab diary should make it possible for you, or another reader, to reconstruct precisely
what you did when you carried out the work, what decisions you made in the process, and
what reasoning lay behind those decisions. Therefore, it should contain:
•
the date, and the title of the assignment
These are obviously needed so that you can find the record later if you need it!
•
a brief introductory paragraph summarising the nature and purpose of the assignment
Read all the way through the script, work out what you are being asked to do and why, and
summarise this in a short introduction. This will ensure that you start the assignment with a
clear picture of what you are trying to do. If, after reading the script, you are still not sure of
the point of the assignment, ask a demonstrator.
•
descriptions of points of procedure not specified in the lab script, with explanation
For example, if the lab script said “measure the diameter several times”, your lab diary should
specify how many times you measured it, and what measuring instrument you used (ruler,
vernier callipers, etc.). This information may be needed to confirm your error estimates and
understand any discrepancies (if you used a ruler while your colleague used callipers, your
measurement errors will obviously be different). You should also explain why you did what
you did: for example, you may have felt that the dominant error in measuring the diameter was
in locating the edge of the image precisely, and therefore there was no point in using callipers
instead of a ruler.
•
notes about any aspect of the procedure that worried you, or any decisions you made
•
•
tables of the measurements you actually
made, not just the derived physical
quantities
For example, you might measure a length on
a photographic image in mm, convert to arc
seconds using a measured or calculated
2
1
conversion factor, and then put this into a 0
formula to derive the mass of a planet. You
need to write down the original length, the
conversion factor, and the converted value,
as well as the final mass. This is critical in
finding and correcting mistakes: for
example, if you mistyped or miscalculated
the conversion factor, it will be much easier
2
1
to correct the problem if you have written 0
down the original lengths. It is also important in getting your error estimates right: the fundamental source of the uncertainty is, after all, the precision of the original measurement.
5
•
estimates of the uncertainty of measured quantities, and the reasoning that led to them
It is not enough just to say “±0.5 mm”: you need to justify this estimate. If the dominant
uncertainty is the accuracy with which you can read your ruler, are you sure you can’t do better
than ±0.5 mm? In the picture, the ruler is marked every 0.2 units, but we can see that the edge
of the grey block is slightly less than halfway between 2.2 and 2.4: we might estimate its length
as 2.28±0.02. This is much more realistic than simply rounding to the nearest scale division
and saying 2.2±0.1.
If the dominant uncertainty is not the accuracy with which you can read your measuring
instrument (and ideally it shouldn’t be – if it is, try to find a more accurate instrument!), then
you should explain what it is: for example, in this picture the irregular edge of the block is the
dominant uncertainty.
If you have made repeated measurements, you may have calculated your error statistically
(as the standard error of the mean), rather than trying to estimate it from first principles. If this
is the case, then say so, and note the number of measurements that you averaged (the standard
error of 10 measurements is more reliable than the standard error of 4).
•
any graphs used to analyse the data, and the results obtained from them
If you use Excel for graphical analysis, make sure that your plots are glued, stapled or
sellotaped into your book – don’t leave them lying around loose. Make sure graphs have axis
labels, including units, and a title. It is useful to number graphs so that you can refer to them.
If the relevant quantity is derived from the gradient of the graph, make sure that the gradient is
quoted, together with its uncertainty and its units (the linest function in Excel will give you the
gradient and intercept of a line with their uncertainties).
•
any necessary diagrams, definitions of symbols, etc.
You do not want to return to the book a week or two later and discover that you have forgotten
whether r refers to the radius of the planet or the radius of its orbit!
•
the sources of any constants or standard values that you looked up
You do not need to copy out all the material in the lab script, since both you and the
demonstrator will have a copy of this, but it is sensible to copy out anything that you need to
refer to or use in calculations, such as an equation or a diagram.
In general, if you have any doubts about whether something should be included or not, put it
in: it is much better to have included something you didn’t need than to have left out
something vital.
4.
How will your lab diary be assessed?
After the end of each session demonstrators will mark lab diaries using the criteria described
in the next section. Please note that while marks are not negotiable, demonstrators will be
happy to discuss marks with students and provide feedback to help improve performance in
future experiments.
.
6
5. Lab Diary Marking
Towards the end of each lab session, your diary will be marked by a lab tutor or
demonstrator, who will briefly discuss the work you have done and highlight any problems.
They will then give you a mark for your work based on the following criteria:
•
Title and Date: clearly indicated
•
Introductory paragraph: aims clearly set out and correct; brief description of task
•
Method: explanation of method; discussion of any special points
•
Progress: good attempt made to complete specified work
•
Measurements: good quality; carefully made, clearly listed
•
Experimental Uncertainties: sensible values; sources of error clearly explained and
estimates justified; mathematical manipulation correct
•
Data presentation (tables): well laid out with column headings and units specified
•
Data presentation (graphs): well presented with good choice of axis and scales;
error bars on points; axes labelled, with units; key or legend if needed
•
Results: good results obtained; quoted to correct precision, with errors and units
•
Conclusions: comparison with standard values with proper account of errors;
discussion of any discrepancies
•
Supplementary questions (if applicable): good answers demonstrating
understanding of material
The following grading system is used:
A: excellent work with only very minor shortcomings
B: good work but with room for improvement
C: barely acceptable work with significant problems
D: inadequate, little effort made
7
SCHEDULE OF LABORATORY ACTIVITY
PHY101 : SEMESTER 1
PHY102 : SEMESTER 2
GROUP
week
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
Introductory Lectures
A
B
C
D
B
C
D
A
C
D
A
B
D
A
B
C
Experimental Uncertainties
Reading Week
EC
EC
P
P
EC
EC
P
P
P
P
EC
EC
P
P
EC
EC
Lecture: Scientific Writing
GROUP
week
1
2
3
4
5
6
7
8
9
10
11
1
P
P
MC
MC
P
AC
AC
AC
2
3
P
MC
P
MC
MC
P
MC
P
Report Writing
P
P
AC
AC
AC
AC
AC
AC
No Lab
Group Problem Solving
All students must make sure that they know which group (1-4) they belong to, and remain in that group at all
times. Groups and laboratory days will be allocated in the first week of each semester.
The physics experiments take place in the 1st Year Teaching Laboratory (D17, Hicks Building).
KEY TO ACTIVITIES
A
B
C
D
P
EC
MC
AC
DC Circuits and Electrical Measurements
Use of oscilloscope
Introduction to computing and applications
Acceleration due to gravity
Experiment from pool
Computing: Excel
Computing -:MathCad
AC Circuits Investigation
8
4
MC
MC
P
P
P
AC
AC
AC
ASSESSMENT AND DEADLINES
Your laboratory work contributes 20% of your mark for each of the two 1st Year Physics
modules (PHY101 and PHY102). The total laboratory mark comprises the following
elements:
PHY101
Lab diary
Computing
Errors Homework
PHY102
60%
25%
15%
Lab diary
Computing
Formal Report 1
Formal Report 2
AC Circuits Investigation
35%
15%
15%
15%
20%
Your laboratory diary is marked at the end of each laboratory session.
The deadlines for submission of assessed work are as follows:PHY101 - Semester 1
Experimental Errors Hwk: 23rd November
Computing assignment: 20th January
PHY102 - Semester 2
Formal Report 1: 7th April
Formal Report 2: 9th May
Computing assignment: 19th May
All submitted work must have the relevant assignment cover sheet attached. These sheets will
be handed out when the assignment is set.
All submitted work is to be handed in at the Physics Office. Late submission will be
penalised.
9
BASIC NOTES ON ERRORS
THESE NOTES ARE INTENDED TO GIVE YOU THE BARE ESSENTIALS.
YOU SHOULD NOTE THE LECTURES GIVEN IN WEEKS 1 OR 6 OF SEMESTER
ONE ON THIS TOPIC, AND ALSO THE BOOKLIST PRESENTED ELSEWHERE IN
THE MANUAL.
STUDENTS ARE EXPECTED TO MAKE CORRECT AND APPROPRIATE USE OF
STATISTICS IN THEIR LABORATORY DIARIES AND REPORTS.
Random Variables
The result of a measurement gives a number which is an example of a random variable
because it is subject to error. Unlike ordinary variables, which just have particular values,
random variables may take on a whole range of values that are spread statistically. Rather
than list them all, it is usually enough to answer two questions:
What is the characteristic value of the variable (or data)? This is given by the
MEAN.
How is the variable (or data) spread about that value? This is characterised by the
STANDARD DEVIATION.
For example, imagine that we take a series of N measurements of some quantity X whose
values we call X1, X2, X3 ... XN which are subject to individual errors and so vary around some
preferred value. If we plot the number of times a particular value occurs against that value
we construct the well-known histogram:
mean
no of results
in an interval
2 standard deviations
value at centre of interval
10
The MEAN, <X>, tells us the average value for our sample of data. We calculate it by
adding all our values and dividing by the sample size:
1 N
X = ∑ Xi
N i=1
The STANDARD DEVIATION, σ, tells us how widely spread the data are about the mean
(as shown on the histogram above). We calculate it by taking the square of all the amounts
2
by which our values differ from their mean (the deviations), (Xi − X ) , finding the mean of
the square deviations, and taking the square root:
 1 N
 ∑ (X − X
 N − 1 i = 1 i
σ= 
)
2
Another name for σ is the root mean square deviation. For normally distributed data, about
68% of values will be within one standard deviation of the mean.
From this the ERROR OF THE MEAN is given by σ / N . The error of the mean is a
measure of the certainty of the average value. As the number of measurements increases, the
uncertainty regarding the average value decreases as the square root of the number of
measurements. However, the distribution of individual measurements will be independent of
the number of measurements taken.
What do we mean by an Error?
If we do an experiment, or measure a quantity, many times, we expect that the values we find
will be distributed about a mean value even if the actual value of the quantity is unchanging.
The standard deviation of the distribution is a good measure of the error. If we can only
make one measurement, we can still estimate the error if we know something about the
limitations of our equipment (e.g. what is the smallest division on the scale? What is the
range of noise in the reading? etc.). Either way we must always quote a measured value with
its error:
X±∆X
where the error ∆X is:
EITHER taken from the spread of measurements
OR estimated from experimental method.
11
Systematic errors
The errors discussed so far are random in nature and so their effect can be minimised by
making repeated measurements. In addition, associated with every measurement will be a
systematic (constant percentage) error due to the accuracy of the equipment used. For
example if a stop watch is used to determine the period of a pendulum random errors may
arise through the starting and stopping of the timing, a systematic error will occur if the
watch is running fast or slow. Systematic errors can only be reduced by the use of more
accurate equipment and not by making repeated measurements. The total error of a
measurement is found by combining the random and the systematic errors in a manner
described below.
Combination of errors
Often we need to measure several quantities and combine them in a final answer. How do we
combine their errors? Here are some simple rules:
1
Adding or subtracting quantities:
If C = A - B then (∆C)2 = (∆A)2 + (∆B)2
2
Multiplying or dividing quantities - work with relative errors.
If C = AB or C =
2
2
2
A
 ∆C 
 ∆A
 ∆B
then 
 =
 +

 C 
 A
 B
B
or, more generally
 ∆C 
If C = AnBmDp then 

 C 
2
2
2
2
 ∆B 
 ∆D 
 ∆A 
= n
 + m  +  p
 + ...
 B
 D
 A
More complicated expressions sometimes combine quantities in both these ways. In all cases
work out and combine the errors in the same order as you work out and combine the
4
quantities. For example if Q = 8π / η(a / L)(p1 − p2 ) then we first work out the error in (p1-
p2) from the errors in p1 and p2 from the addition rule, then combine with the errors in a and L
using the multiplication rule.
NB sometimes you will see an absolute error quoted. This is a statement of the largest
possible error, not a root-mean-square error as discussed above. Absolute errors are
12
combined in a different way: we add their moduli directly rather than squaring, adding and
square-rooting.
13
LEAST SQUARES FIT
The straight line
In an experiment it is often the case that one quantity y is a function of
another quantity x, and measurements are made of pairs of values of x
and y. The values are then plotted on a graph and we try to find a
curve corresponding to some algebraic function y = y(x) which passes
as closely as possible through the points. We shall only consider the
case where the function is the straight line
y = mx + c
(1)
The problem is to calculate the values of the parameters m and c for
the best straight line through the points.
The straight line relation covers a great range of physical situations. In
fact we usually try to plot the graph so that the expected relationship is
a straight line. For example, if we expect the refractive index µ of a
certain glass to be related to the wavelength λ of the light by the
equation
µ = a + b/ λ2
(2)
we plot µ against 1/λ2.
The method of least squares is the standard statistical method for
calculating the best, i.e. most probable, line through a set of points.
Suppose there are n pairs of measurements (x1, y1), (x2, y2)...(xn, yn) as
shown in Fig 1. Assume that the errors are entirely in the y values.
(This assumption is very often correct. When it is not, the analysis is
much more complicated). For a given pair of values for m and c, the
deviation of the ith reading is
yi - mxi - c
(3)
y
x
Fig. 1 Method of least squares. The best line through the points is
2
taken to be the one for which ∑ (yi − mxi − c) is a minimum.
14
The best values of m and c are taken to be those for which
S = ∑ (yi − mx N − C )
2
(4)
N
is a minimum - hence the name:- method of least squares.
The principle of minimising the sum of the squares of the deviations
was first suggested by Legendre in 1806. We have already seen that in
the case of a single observable the principle gives the mean as the best
value.
From equation (4)
∂S
= − ∑ 2 x N (y N − mx N − c) = 0
N
∂m
∂S
= − ∑ 2(y N − mxN − c ) = 0
∂c
N
(5)
(6)
Therefore the required values of m and c are obtained from the two
simultaneous equations.
m∑ x 2N + c ∑ x N = ∑ x N y N
(7)
m∑ x N + cN = ∑ yN
(8)
N
N
N
N
N
Solving gives:
Slope
m=
N ∑ x N yN − ∑ x N ∑ y N
N
N
(9)
N ∑ x − ∑ xN ∑ xN
N
N
N
∑y ∑x −∑x ∑x
c=
N∑ x − ∑ x ∑x
2
N
N
Intercept
N
2
N
N
N
N
N
2
N
N
N
N
N
N
yN
(10)
N
N
15
An estimate of the errors in slope and intercept can be obtained from
the variance, σ2(x), of each quantity. Thus
σ 2 (m) =
∑ (y
− mx N − c )
2
N
N
N
N − 2 N ∑ x 2N − ∑ x N ∑ x N
N
N
σ 2 (c ) =
N
2

− mxN − c ) 
∑N x ∑N x


N
N
 1+ N x 2 − x
N (N − 2 )
x 
∑
N
∑
∑

N
N N
N 
N
∑ (y
N
(11)
N
(12)
Alternatively
∑ ( y N − mx N − c )
2
σ (c) =
2
Calculations
N
N (N − 2)
+
∑x ∑x
N
N N
2
N
N
σ 2 (m)
(13)
Most modern scientific calculators have linear regression built in as a
standard function. You should check your calculator and learn to use
these functions if they are available.
Alternatively, the computers in the first year laboratory have spreadsheet software installed on them (Microsoft Excel), which allows
plotting of graphs and calculation of gradient and intercept with
associated errors.
You are recommended to use these.
A demonstrator will show you what to do.
16