Fall 2017


PHYSICS 3081, 4051




Prof. Morgan May, 616 Pupin, may@phys.columbia.edu

Prof. Elena Aprile, 1016 Pupin, age@astro.columbia.edu


Teaching Assistants:

Joseph Howlett jh3226@columbia.edu

Max Abitbol mabitbol15@gmail.com

Kenneth Sikes kenneth.sikes@gmail.com

Dr. Ben Nachumi peripatetic1@yahoo.com







The Laboratory offers a series of fundamental experiments in various fields of physics, as listed below. In addition, special projects, leading to new experiments for the lab, can be undertaken, under the guidance of a faculty member, by appropriately qualified students.


Selecting an underlined title downloads a pdf file, which can be read with Adobe Acrobat Reader.


1. Counting Statistics and Artificial Radioactivity and getting started see also Rainwater and Wu 1 , 2 and readings

2. Coincidence Counting (see also readings)

3. Electron Diffraction , Charge on the Electron and getting started see also Millikan, Steven Weinberg, Martin Perl and Brian Greene

4. Fraunhofer Diffraction see also mercury spectrum , Vernier scale

5. Gamma--ray Crystal Spectrometer and X--ray Fluorescence and getting started see also Moseley's Law (Tipler)__  and readings

6. Laser (see also laser principles , Fabry Perot manual and notes on laser setup )

7. Laser Tweezers , Brownian Motion, Brownian Motion Analysis

8. Michelson Interferometer, Fabry Perot Interferometer and Channeled Spectra see LISA for an interesting application

9. (Mossbauer Effect)

10. Muon Lifetime see also Muon Lifetime Corrections , Cronin on cosmic rays, background rate calculation, Cosmic rays,

     LeCroy 9301 setup and readings

11. Nuclear Magnetic Resonance and getting started see also Feynman , Tipler ; for an interesting application

     see Emlyn Hughes xenon NMR for lung imaging

12. Optical Pumping

13. Quantum Hall Effect Manual see also  Quantum Hall Effect Notes , software , Feynman , Horst Stormer , Laughlin, and topology

14. Vacuum and Mass Spectrometer

15. Quantum Conductance see also Procedure , QC Analysis , van Rutenbeek and Igor Manual

16. Gravitational Lensing - see tesla website

17. Superconductivity

18. Scanning Tunneling Microscope

19. Cosmic Microwave Background



Also consult http://tesla.phys.columbia.edu:8080/eka/




An important part of the laboratory experience is to acquire a good understanding of the treatment of measurement errors. Below is a list of references.

1. Lyons L., “Statistics for Nuclear and Particle Physicists”, Cambridge University Press, 1999.  Some excerpts can be viewed by clicking on the links: Random and Systematic Errors , Standard Deviation and Combining Errors , Least Squares Fitting

2. Taylor, J. R., “An Introduction to Error Analysis”, University Science Books, 1997.

3. W.R. Leo, “Techniques for Nuclear and Particle Physics Experiments”- Chapter 4 Statistics and the Treatment of Experimental Data, Springer, 1994.

4. Young, H. D., “Statistical Treatment of Experimental Data”, McGraw--Hill , 1962.

5. Beers, Y., “Introduction to the Theory of Error”, Addison--Wesley , 1953.



Full course attendance requires completion of two experiments in a semester for 2 points of credit. Experiments are often performed by student pairs. When students work together they help each other in the setting up and the taking of data. Partners can confer and compare their work, but each partner is separately responsible for all calculations and data analysis, and for an independently written report.

The first class is an introductory session.  Following this session attendance in the Laboratory course typically progresses as follows:

1. Select an experiment, schedule a starting date, and pick up experiment instructions and auxiliary written material at least one week before starting lab work.

2. Work in the laboratory (1 to 5 pm) on consecutive weeks, typically 3 or 4, until the experiment is completed. Only register for the laboratory if you have no time conflicts during the 1-5 pm period. Start finishing up your data taking for the day at 4:45, so that the lab can end promptly at 5:00

3. After preliminary analysis of your data confer with one of the instructors before writing a full report. The final report may incorporate instructor’s suggestions as well as any additional material student deems necessary. Final report for the first experiment is due on or before seven days after midterm date.

4. You may not start the second experiment until the final report for the first experiment has been received by an instructor.

5. The second experiment must be started in time to complete a preliminary analysis of your data  and confer with one of the instructors by the last day of classes. Final report is due within seven days of final day of classes (or before the first day of final exam period which ever comes first).

6. Students will make a short presentation to the class about one of their experiments. One set of presentations will be scheduled in mid semester, and a second set near the end of the semester

6. Grades are based on lab work-overcoming difficulties on your own, preparedness, technique and persistence – as well as on reports and presentations.




There is a single set--up for each experiment, and a student is expected to work on it for at least two 4--hour laboratory periods, although four periods are usually necessary, especially for students with no previous laboratory experience or taking Physics W3081 for the first time. When scheduling an experiment for a set of consecutive dates, the student will be given specific laboratory instruction sheets as well as references and supplementary reading.

All the experiments utilize equipment which will be unfamiliar to most students but several of them rely on physical principles and techniques which should be in principle familiar. In practice these principles and techniques have been usually forgotten or only very superficially understood.

It is absolutely essential to begin preparation for an experiment at least one week before doing work in the laboratory, in order to allow time for extensive reading from the suggested sources. There may also be preliminary calculations to be made. We strongly encourage consultation with instructors before the first scheduled laboratory session; the introduction by the instructor at that session will assume substantial preparation by the student.



Standard notebooks, with alternate white and yellow pages and carbon paper, are available in the book store. All of the experimental data are to be entered in the notebook.

The notebooks should contain the measurements made during the experiment, as well as appropriate diagrams for the set--up (including names and identifying numbers of pieces of equipment), explanatory notes as to how measurements were made, and pertinent qualitative information. Keeping a complete notebook is an important feature of all experimental research; inaccurate documentation of experimental facts leads to waste of time, frustration and invalid analysis.

Some attention should be paid to keep the data book neat and orderly. Paying too much attention to neatness might appear as an unnecessary waste of time, however, two weeks later, when you try to figure out what you were doing earlier in the lab, it will make your job much easier. The aim of data taking is to record all of the pertinent information and directly measured numbers. Try to use some simple rules.

Use legible hand writing. Always enter complete information, do not assume that what you enter is obvious and that you will remember later what you were doing at the time. Have your entries well labeled and commented, and in tabular form where appropriate. Don't worry about recording data which may later be rejected as preliminary or incorrect; simply cross out what you don't want. Writing on scrap paper and later copying into the laboratory notebook is very bad practice. For those experiments where data is collected by a computer, print sample listings of the data, and tape the printout to the book. The printout should be properly labeled and the data neatly formatted and compressed. The main data body should in this case be copied in a form which you can analyze on the laboratory computers, on your home PC or on the various such facilities made available to students at Columbia.



Preliminary Run--Through. You should always begin with a very simple preliminary run of the experiment and some quick calculations of the final result you are trying to obtain. This helps you to understand how the equipment works and to see the general magnitude of the observations, before attempting to perform accurate and complete measurements. If you have problems at this level ask the instructors.

Significant Figures. The use of digital instruments and calculators often leads to recording long string of insignificant digits. This not only entails unnecessary writing and produces clutter in your book, but also gives incorrect indication of unjustified accuracy. An entry such as 6.50 X 10^-19{units} (what could that be?), with an indication of the uncertainty, is an appropriate form for the result. Keep only enough significant digits to assure that no accuracy is lost. No more, no less. This implies an awareness on your part of the errors associated with the measurement.

Data Reduction and Error Analysis A correct treatment of uncertainties is often the most important and most difficult part of data analysis in experimental physics. An extensive treatment is required for many of the experiments in this course; a less extensive but still significant treatment is required for the others. References and notes on statistics and the theory of error analysis will be available; it is important to study this material in depth.

Preliminary Review of the Analysis. After each laboratory session (or during the session itself) you should examine and briefly analyze the data to see whether it is self--consistent and gives sensible results. This will permit you (if necessary) to repeat or check some measurements in the next session if discrepancies are found. In any case, after the last session and before preparing the full report, you should complete a preliminary analysis of the data and meet with the instructor to go over the results. This often reveals deficiencies in the data or analysis which can be corrected before the full report is submitted.

Laboratory Reports. Although carefully written reports are a major requirement of this course, lengthy theoretical derivations should absolutely be avoided. Only discuss the basic principles, a page of introduction at most. The written part of the report should briefly describe your measurements, referring to but not repeating the material in the instruction sheets (which are to be included in the report along with data sheets) as well as to other sources that you have read.



Report Style

(Some of what follows is an abbreviated extraction from the APS (American Physical Society) style manual)

(Report preparation is an important aspect of scientific activity. To facilitate this process computers, printers, a digital camera, and appropriate software are available. The finished report should be in such form as would be acceptable (in principle) for publication in a scientific journal.)



Course number


Author: (Author’s name)

Partner: (Partner’s name)


(One self-contained paragraph: a brief statement of what was measured and calculated.)

The main body of report (text and math) should be divided into sections with the use of section headings and subheadings. Equations, tabular material, figures, and references should follow a sequential numerical scheme in order to ensure a logical development of subject matter. In the body of the paper all references, figures, and tables must be cited consecutively in numerical order. Tabular material and figures should be placed in the body of the report in reasonable proximity to where they are first cited. Equations that are important, long, complex, or referenced later in the report are set off from the text (displayed) and may be numbered consecutively with Arabic numbers within parenthesis [(1), (2), (3), etc.]. These numbers are placed to the extreme right of the equation.

Each table or figure must have a descriptive concise caption. The table (figure) caption must begin with the word table (figure) in capital letters followed by the appropriate Roman numeral and period, and then a small amount of explanatory text.

The main body of the report should begin with a section labeled Introduction and close with a section labeled Conclusion. The report should be self-contained and complete. Attached to the report should be Appendices which contain: laboratory instruction sheets and handouts, work sheets from your laboratory notebook, expanded tables and figures.




It is recommended that you look at typical research journals to get an idea of how the scientific community presents reports. An excellent example of such a journal is The Physical Review.

All reports are to be submitted by email.

Complete your analysis of first experiment and confer with instructor before midterm date.

Report of first experiment is due on or before seven days after midterm date .

Complete your analysis of second experiment and confer with instructor before last day of classes.

Report of second experiment is due within seven days of final day of classes (or before the first day of final exam period which ever comes first).