1. 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.

2. 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. 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%). 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.

3. An interesting answer given in “Quora” I strongly disagree and definitely do not want you to give this kind of answer from now on.

4. 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.

5. Fitting data to a straight line Can you give any guideline to choose y(x) or x(y)? There are two way to represent the same straight line: We would like to hear the opinions from two students.

6. Fitting data to a straight line 1.Thermal expansion coefficient (length vs. temperature) of an Al rod. 2. Non-linear Kerr rotation(  ) vs. temperature(T): Sr 2 IrO 4 (a previously cited example) In these two cases, which physical parameter(s) is under our control? There are two way to represent the same straight line: Can you give any guideline to choose y(x) or x(y)?

7. Fitting data to a straight line What the figure will look like in a T vs.  plot? 1.Thermal expansion coefficient (length vs. temperature) of an Al rod. 2. Non-linear Kerr rotation (  ) vs. temperature (T): Sr 2 IrO 4 In these two cases, which physical parameter(s) is under our control? Please sketch T vs.  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.

8. Fitting data to a straight line What the figure will look like in a T vs.  plot? Non-linear Kerr rotation (  ) vs. temperature (T): Sr 2 IrO 4 This is the figure after rotating it by 90 degrees. Then flipped horizontally. Does it look weird?

9. Fitting data to a straight line Can you give any guideline to choose y(x) or x(y)? There are two way to represent the same straight line: 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.

10. Fitting data to a straight line The deviation d i between each of the measured values y i and the corresponding calculated values. Thus for a linear equation: Commonly, the deviation (  i ) of each y i -value is different. chi-squared of the data: sum of weighted deviations The best fitting means minimizing with respect to some variables? Can you tell us what are the variables?

11. Fitting data to a straight line Minimizing with respect to a and b. Define: where Several math steps

12. Fitting data to a straight line The standard deviations are, (note: uncertainties are on y i; a and b are function of y i.) Let us calculate the second one. Finally, Consider the case of i =1 first. General case of i. Sum over all i‘s.

13. 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.

14. 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.

15. 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.

16. Expected equation for thermal expansion: Before using “black box” software, it is wise to estimate the parameters the old- fashion graphical way first The initial guess yields intercept/slope