This semester I’ve been teaching foundation year students in experimental physics. The goal for them is to find a laser’s wavelength through diffraction experiments. Because of the covid-19 pandemic, restrictions imposed by the University don’t allow the students in labs, so I have to carry out the experiment, filmed with different cameras and broadcasted to the students at home. The far-from-ideal situation led to poor accuracy in the measurement readings, hence a substantial errors on each of their measure. I’ve noticed that this was a source of issues, as many sent me e-mails or came to the drop-in session, to understand why their measurements did not match the expected value. This actually leads to some interesting discussions about experimental errors. I’d like to share some of this.

### Why we estimate errors

The foundation year students come to the class with the (justified) feeling that the job is done once they obtain a numerical value for the quantity we ask them to measure or calculate. This is different at university, as we are also concerned with the accuracy of the measurement. The accuracy is expressed with an experimental error on the measurement. As we, scientists, are interested in measurements for the sake of comparing them with different experiments, theories, or use them to predict new behaviours, the value of the error becomes crucial to the interpretation of the result. Let me develop this.

In my lab, the students are asked to find the wavelength of a laser. We give them the laser specification (including the wavelength), and most of the time, they get something different from the specification. The laser’s wavelength is supposed to be 532nm (green light beam). When they measure 528nm, how can we get an evidence for a discrepancy? Can we conclude directly that the laser’s specification is inacurate? There could be 3 possibilities:

### What it means in undergrad labs

In the lab, the uncertainty is an essential value to judge the accuracy of a measurement, that makes us able to judge of the quality of a measure. There are good practices to mitigate the influence of errors and reduce the uncertainty of a measurement. The first is to analyse statistically, whenever it is possible, the value, and consider only the mean values, with the associated uncertainty. Second, I would also recommend to record everything that could be relevant to the problem on a neat notebook. It becomes all the more important in the remote lab to write down results manually, with an estimation of their uncertainty, as soon as they are collected: you cannot mitigate errors if you don’t record them in the first place.

### references

• Data Analysis for Physical Science Students, L. Lyons, Cambridge University Press 1991
• Practical Physics, G. L. Squires, Cambridge University Press 2001