Writing a Lab Report

PHYS 4321/4322 · Advanced Lab

Andrew J. Steinmetz

Who you are writing for

Your report is a standalone technical document, not a worksheet attached to the lab manual.

Your reader

Has your physics training
Has not read the manual
Cannot see your apparatus

Your job

Explain the physics
Explain why each step was done
Be detailed enough to be reproduced and trusted

Content matters more than length. You are the expert here.

Anatomy of a report

Section
Title, authors, affiliation, date
Abstract
Introduction
Theory
Experimental methods
Data and analysis
Discussion
Conclusion
References
Appendices

The abstract

Lets a reader decide whether to read the rest.

The topic of the experiment
The technique(s) used
The result, with its uncertainty

Write it last, and plan enough time to write the report at all.

Introduction and theory

Introduction

Motivate the scientific question
Give the historical context
Enough physics that the motivation lands
Mention a modern use of the same physics

Theory

Set up the problem, define terms
Main steps and approximations, not every line of algebra
Long derivations go in an Appendix
Number your equations

This is where the reader sees your background work and can themselves be brought up to speed.

Experimental methods

Do

Explain how the apparatus works
Include a schematic with every critical part labeled
Simple functional boxes
Reference the figure early

Don’t

Draw every knob and cable
Write an instruction manual
Recite a parts list
Say “we used the setup in the manual”

A diagram that helps you perform the experiment usually does not help a reader understand it. This likely requires you to draft your own diagram.

Figures, tables, and data

Every figure and table

Numbered sequentially, figures and tables counted separately
A caption defining symbols and stating conditions
Referenced in the text, and ideally discussed
Column headings descriptive, units in the heading

Every plot

Axis labels with units
Even divisions at round values: 0.5, 1.0, 1.5, etc.
SI prefixes, not long decimals: 0.5 mA, not 0.0005 A
Data as symbols, fit as a line, same axes
Error bars on every point

Uncertainties and results

Every measured value gets an uncertainty, and so does every value you take from elsewhere
So does every derived quantity: \(h\), \(e/m\), wavelength \(\lambda\), etc.

Explain how you determined it. A sample calculation in the Appendix may be appropriate.
Compare to accepted value: does your data fit, or why not?
Percent error is rarely helpful

Write this:\(\quad G = (6.674\,30 \pm 0.000\,15) \times 10^{-11}\ \mathrm{N\,m^2/kg^2}\)

Not this:\(\quad G = 6.674\,30 \times 10^{-11}\ \mathrm{N\,m^2/kg^2} \pm 1.5 \times 10^{-15}\ \mathrm{N\,m^2/kg^2}\)

Round the uncertainty first to one significant figure, two at most. Then round the value so that it stops at the same decimal place.

Where uncertainty comes from

Statistical (random)

Measurement-to-measurement scatter
\(s\) is the scatter of individual measurements
\(\sigma_{\bar{x}} = s/\sqrt{N}\) is the uncertainty of the mean — this is what you report
Shrinks as you take more data

Systematic (instrumental)

Calibration, zero offset, instrument accuracy, temperature
Analog: half the smallest division. Digital: one unit of the last digit, or the manufacturer spec
More data does not help

Taking 10,000 readings with a miscalibrated voltmeter does not fix the calibration.

Propagating uncertainty

For \(f = f(x_1, x_2, \ldots)\) with independent uncertainties:

\[\sigma_f^2 = \sum_i \left(\frac{\partial f}{\partial x_i}\right)^{2} \sigma_i^2\]

If	Then
\(f = x \pm y\)	\(\sigma_f = \sqrt{\sigma_x^2 + \sigma_y^2}\)	Absolute uncertainties add in quadrature
\(f = xy\) or \(x/y\)	\((\sigma_f/f)^2 = (\sigma_x/x)^2 + (\sigma_y/y)^2\)	Fractional uncertainties add in quadrature
\(f = x^n\)	\(\sigma_f/\lvert f \rvert = \lvert n \rvert\, \sigma_x/\lvert x \rvert\)	A power scales the fractional uncertainty

Statistical and systematic terms combine the same way: \(\sigma_\mathrm{total}^{2} = \sigma_{\bar{x}}^{2} + \sigma_\mathrm{inst}^{2} + \cdots\), reported as \(x_\mathrm{best} \pm \sigma_\mathrm{total}\) with units.

Discussion and conclusion

Discussion

Do your results agree with the accepted value?
If not, why — with a calculation or a reference, not a shrug
Name the dominant source of error

Conclusion

Short summary of what you did and found
Repeat the results with their uncertainties, digits, and units
What the experiment opens up

Inspect each term in the propagation of error separately. The largest one is what “suggestions for improvement” should target.

Style and typesetting

Suggestion: Use LaTeX in Overleaf, available through Georgia Tech, with the APS RevTeX template.

Write this	Not this
\(c\)	c
\(c = 2.998 \times 10^8\ \mathrm{m/s}\)	\(c = 2.998 \times 10^8\, m/s\)
\(m\lambda = d \sin\theta\)	\(m\lambda = d sin \theta\)
\(2.3 \times 10^5\)	2.3e5
\(B^2\), \(B_2\)	B^2, B_2

Real superscripts and subscripts using LaTeX e.g. x^{2}_{i} for \(x^{2}_{i}\)
Number your sections so you can point back to them
Proofread. Careless writing counts against you

The point of style and typesetting is to look nice. A nice looking document is easy to read and conveys information without much visual friction.

Citations

Cite it

Anything from anywhere including the lab manual
What another person told you
Numbered in citation order [1]
Peer-reviewed or academic sources, not Wikipedia

Let BibTeX do it

@article{LIGOScientific:2016aoc,
    author = "Abbott, B. P. and others",
    collaboration = "LIGO Scientific, Virgo",
    title = "{Observation of Gravitational Waves from a Binary Black Hole Merger}",
    eprint = "1602.03837",
    archivePrefix = "arXiv",
    primaryClass = "gr-qc",
    reportNumber = "LIGO-P150914",
    doi = "10.1103/PhysRevLett.116.061102",
    journal = "Phys. Rev. Lett.",
    volume = "116",
    number = "6",
    pages = "061102",
    year = "2016"
}

Cite it with \cite{LIGOScientific:2016aoc}. Journal pages, INSPIRE-HEP, Google Scholar, and NASA ADS export these for you. Otherwise, you may need to write your own BibTeX/references.

[1] B. P. Abbott, et al. Phys. Rev. Lett. 116, no.6, 061102 (2016). doi:10.1103/PhysRevLett.116.061102 arXiv:1602.03837 [gr-qc]

Academic integrity

Two ways to plagiarize

Literal — copying a sentence and swapping a few words. Cosmetic edits do not save you.

Intelligent — restating someone’s idea as your own. Rewriting removes the copying, not the need to cite.

Where it happens

The Introduction, most often — it is the hardest section to write
Quote directly, or write it in your own words; either way, cite it
A paragraph stitched from quotes is not an original contribution

Do not work from previous years’ reports. In doubt? Ask.