Conversation with one student
After last week lecture, one student told me that he/she received a “poor” grade
from the first lab. If you were the student, what would have been your response?
1) Sad ; 2) Appreciative.
Conversation with one student: the results
In 2014, my first time of teaching Phys 2605, following the previous tradition
First week, lab orientation
Second and third weeks, conducting first lab
Forth and fifth weeks, conducting second lab, TA will collect the first lab book at the beginning
of the forth week.
In most cases, TA will return your first lab book at the beginning of the six week (beginning of
the third lab).
By the time you reviewed your graded lab book and tried to make changes accordingly, similar
“mistakes” already appeared in both first two lab books which were 2/5 of your lab book scores.
In 2015, a tight grading schedule for the first two labs was implemented
to improve the quality of lab reports. TA’s observation: majority of the
student’s lab books showed significant improvements.
This year, the conversation with one student lead me to take the
following changes, heavier weights for the latter lab reports:
Lab 1 (5%); Lab 2 (10%); Lab 3 (25%); Lab 4 (30%); Lab 5 (30%).
An interesting answer given in “Quora”
I strongly disagree and definitely do not want you to give this kind of answer from now on.
A linear function
The linear function w = a*u + b is a very general one for many different situations,
e.g., w = y, ln(y), ln(y-c), etc. and u = x, sin(x), ln(x), 1/x, ln(x-d), etc.
Examples that we discussed
in the previous lecture.
Fitting data to a straight line
There are two way to represent the same straight line:
Can you give any guideline to choose y(x) or x(y)?
We would like to hear the opinions from two students.
Fitting data to a straight line
There are two way to represent the same straight line:
Can you give any guideline to choose y(x) or x(y)?
1. Thermal expansion coefficient (length vs. temperature) of an Al rod.
2. Non-linear Kerr rotation(q) vs. temperature(T): Sr2IrO4 (a previously cited example)
In these two cases, which physical parameter(s) is under our control?
Fitting data to a straight line
1. Thermal expansion coefficient (length vs. temperature) of an Al rod.
2. Non-linear Kerr rotation (q) vs. temperature (T): Sr2IrO4
In these two cases, which physical parameter(s) is under our control?
What the figure will look like in a T vs. q plot?
Please sketch T vs. q in your paper along with error bars
from four representative data points. Three students
have been picked to plot the figure on the white board.
Fitting data to a straight line
Non-linear Kerr rotation (q) vs. temperature (T): Sr2IrO4
What the figure will look like in a T vs. q plot?
This is the
figure
after
rotating it
by 90
degrees.
Then
flipped
horizontally.
Does it look
weird?
Fitting data to a straight line
There are two way to represent the same straight line:
Can you give any guideline to choose y(x) or x(y)?
For the given experimental measurement, usually x is the variable that we
have a better control with a smaller error and y is the physical property
that is measured and tends to have a larger error. We always try our best
to estimate the errors on both x-values and y-values.
Fitting data to a straight line
Thus for a linear equation:
The deviation di between each of the measured
values yi and the corresponding calculated values.
Commonly, the deviation (si) of each yi -value is different.
chi-squared of the data: sum of weighted deviations
The best fitting means minimizing
Can you tell us what are the variables?
with respect to some variables?
Fitting data to a straight line
Minimizing
with respect to a and b.
Define:
Several math steps
where
Fitting data to a straight line
The standard deviations are,
(note: uncertainties are on yi; a and b are function of yi.)
Let us calculate the second one.
Consider the case of i =1 first.
General case of i .
Sum over all i‘s.
Finally,
Example: Hypothetical Data
• Imagine we are setting up to use an interferometer to measure
optical path lengths through different materials.
The interferometer is built on a platform of metal (we don’t
know the composition) and we are worried about the effects of
thermal expansion. To assess the potential systematic error (and
determine the required level of temperature control), we measure
the deviation of the platform with temperature from its length at
15.0° C, which the manufacturer tells us is 1.50000 meter.
• Expectation: within a small temperature range, the thermal
expansion should be linear, with a single parameter α, the
coefficient of linear thermal expansion.
The first step was to enter our fictitious data into an Excel spreadsheet and make a graph
(Appendix C in your lab manual, we will discuss some of the features soon).
Uncertainties are estimated based on experience, specs from manuals, or careful examination
of apparatus and procedures. Alternatively, we could do a statistical assessment (repeated
measurements) and determine the random uncertainties from the observed standard
deviations. We will discuss this issue later in the semester. Most important: explain clearly in
your log book where you get errors and be alert for evidence that your estimates might be
wrong. For our fictitious example I made up the (plausible) uncertainties plotted below.
Expected equation for thermal expansion:
More realistic equation: any suggestion?
Write done your answer in your paper.
Two students has been picked to write
their answers on the white board.
Expected equation for thermal expansion:
Before using “black box” software, it is wise to estimate the parameters the oldfashion graphical way first
The initial guess yields
intercept/slope