PHYC 307L: Junior Laboratory

Prof. F. Elohim Becerra
Office: PAIS 2514
Phone: 505 277-2673

Teaching Assistant
Caleb Annan
Office: PAIS B11XX

Description of the class and objectives

The Junior Lab 307L is a laboratory course with experiments in modern physics for advanced undergraduate students. Students will obtain expertise in laboratory equipment, data analysis, error analysis and in writing formal reports in a scientific format. The course consists of one lecture per week and one 3-hour lab session per week. Students will perform experiments for the measurement of fundamental constants and experiments related to Modern Physics. The lectures will be focused on statistical tools and techniques for error analysis and data reduction for interpretation of the experimental results.

Pre-requisites: Calculus, Basic elements of statistics; Computational tools, Basic electronics and optics. (PHYS 2415 required)

Lectures: Monday, 13:00-13:50, Room PAIS 1140

Lectures will cover topics related to elements of statistics and error analysis for the proper treatment of the experimental data. See Topics for details.


Lab Sessions: Monday, 14:00-16:50, Room PAIS 1405.

You must complete 6 experiments from the list below (one every two weeks), plus the oscilloscope experiment (one week), which is mandatory. For the experiments, you will use guides from the Junior Lab manual from Prof. Michael Gold, but some experiments have been updated. The updated guides for the experiments to be followed are:

Each experiment will be scheduled for two weeks. Students need to schedule the experiments in advance to ensure availability. There will be a calendar kept by the instructor and the TA.

* For each experiment, you will need to investigate/study and understand the physics behind the experiment, the technical aspects of the setup and their functionality, how the experiment and each part of the setup works, and realize proper data and error analysis to obtain the result. By design, the lab guides are brief, and students are expected to investigate more in depth the physics, theory, and technical aspects of the experiments.


The lectures will be based on several books (mainly based on  Bevington & Robinson, and  Melissinos Ch10). Below are some very good references for statistics and modern physics.

Additional resources
Experiments in Modern Physics (Academic Press, 2nd Edition): Adrian C. Melissinos, Jim Napolitano.
Fundamentals of Photonics 2nd Edition: E. A. Saleh, Malvin Carl Teich.

Office hours. You may arrange a meeting with the instructor via email.
TA office hours: You may also arrange a meeting with the TA via email.


  1. Homework 10%
  2. Lab Notebook 40%
  3. Formal Reports: 40% (2 in total)
  4. Oral presentation: 10%

Homework: There will be regular assignments related to basic statistics, error analysis, curve fitting and basic programming. The assignments will be given throughout the semester, about one per week, and will be posted in the Tentative Schedule. Assignments are due at the beginning of the class. Homework is individual; you may not copy another student's work.

Lab Notebook: You will keep a lab notebook where you will describe the experimental procedure and perform the data and error analysis. The guidelines are here: Lab notebook Guidelines.

Formal Reports: You will write two formal reports from two experiments that you performed in the laboratory. The guidelines are here: Formal Report Guidelines..
Lab reports should be typed and submitted as a word or PDF document by email with the subject “Lab Report #” followed by the number of the lab report, for example “Lab Report #1". The file name should be your last name followed by the name of the experiment. Lab reports are individual (i.e. each person needs to submit their own).
Draft of Lab report #1 will be reviewed and returned to you to make revisions.
Published physics papers such as in Physical Review Letters, Optics Letters, etc. provide a good guide for writing your lab report. Any research article is good example. One example from a class report is here.

IMPORTANT: Use your own words. Do not copy from your classmates or any other resource, including lab guides. This is considered Academic Dishonestiy. Instead, read, understand and write with your own words. Scientific papers are the product of your understanding and your own work, and not of other people's work.

Presentation: Each student will give a presentation at the end of the semester about an experiment (12 minutes+ 3 for questions). It should duscuss applications of the subject studied to science and/or technology. Some tips; more tips.

 Due Dates

Date Description
02/26 (M)
02/28 (W)
Lab notebook with Experiments 1 & 2
Draft of 1st Formal Report (via email 5pm)
03/19 (M) 1st Formal Report (via email 5pm)
04/01 (M) Lab notebook with Experiments 3 & 4
04/29 (M) Lab notebook with Experiments 5 & 6
2rd Formal Report (via email 5pm)

The lab notebooks and homeworks must be submitted in class (lecture time) on the day they are due. 

Late work policy:
Late work assignments will be accepted but with a 15% penalty for each day past the deadline. So any work handed-in within 24 hrs of the deadline will carry a 15% penalty, one handed-in within 48 hrs will carry a 30% penalty, as so on.

Lecture Topics

Tentative list of topics that will be covered. The calendar is in the Tentative Schedule.

  1. Introduction:
    - Overview
  2. Errors and parameter estimation: (Bevington Ch1&Ch2)
    - General properties; Estimation of a parameter; Mean and Variance
  3. Statistical Distributions (Bevington Ch2, Melissinos Ch10.1-2, Taylor Ch5,Ch10&Ch11)
    - Basic distributions; Binomial; Poisson; Gaussian
  4. Propagation of errors (Bevington Ch3;, Taylor Ch3; wiki)
    - Error propagation; Correlated variables; Errors of basic operations
  5. Maximum Likelihood Estimation (MLE) (Bevington Ch3, Melissinos Ch10.3-4; wiki)
    - Maximum Likelihood; Mean and variance of a distribution; Standard deviation of the mean; Weighted average
  6. Maximum Likelihood Estimation (Bevington Ch6, Melissinos Ch10.3-4)
    - Fit to a straight line; Estimated parameter; Standard deviation of estimated parameters
  7. Nonlinear Fitting (Bevington Ch8)
    - MLE application to a nonlinear function with multiple parameters
  8. Goodness of a fit (Bevington Ch3)
    - Test of a fit; Chi square; t-student distribution
  9. Mote Carlo Simulation (Bevington Ch5)
    - Generation of random data; treatment of errors and fits
  10. Advanced topics (Taylor Ch9)
    - Bias of an estimator; Error matrix and correlated systems
  11. Modern Optics
    - If time allows, we will discuss some special topics such as lasers, coherence, nonlinear optics and quantum optics.

Additional resources

Class overview: Lecture 1

Fit straight line with unequal errors

Statistical Treatment of Data

Advice for physics speaker

Program examples

Fit to a Lorentzian

Tentative Schedule

Lectures Date Subject Reading Homework HW Due Notes
  01/15 (M) MLK (no class)        
L1 01/22 (M) Overview; Measurements and Uncertainties Bevington CH1-2 HW1 (M) Jan 29  
L2 01/29 (M) Probability distributions Bevington CH1-2 HW2 (M) Feb 5  
L3 02/05 (M) Propagation of Errors Bevington CH3 HW3 (M) Feb 12  
L4 02/12 (M) Maximum Likelihood Estimation (MLE) Bevington CH4      
L5 02/19 (M) Fit to a straight line with MLE (I). Bevington CH6 HW4 (M) Feb 26 Equations line fit
L6 02/26 (M) Weighted average. Standard error of the mean. Melissinos CH10 HW5 (M) Mar 04  
L7 03/04 (M) MLE error estimation. Example, fit to a straight line Melissinos CH10 Bevington CH6      
  03/11 (M) Spring Break        
L8 03/18 (M) Fit to nonlinear functions: Linearization Bevington CH7-8      
L9 03/25 (M) Fit to nonlinear functions Bevington CH8 & 11      
L10 04/01 (M)          
L11 04/08 (M)          
L12 04/15 (M)          
L13 04/22 (M)          
L14 04/29 (M)          
L15 05/06 (M) Finals Week