# Physics 107 - More on Uncertainty

Uncertainty Everywhere

As you have seen, uncertainty in your measurements can take a variety of different forms and this lab is intended to give you practice in several different situations that you might encounter in the future. You will work in pairs and take turns trying out the different apparatus. Make sure you have taken a turn on at least one of the ‘Group A’ measurements in the first 1.5 hours of the class since they are the more time-consuming ones.

For each exercise that you perform you should evaluate what the dominant source of uncertainty is and suggest ways to improve the measurement.

Group A Measurements

Exercise I: a noisy electrical measurement

A function generator has been arranged so that it produces a voltage difference that varies randomly. This is an artificial version of electrical noise, which is a phenomenon that is often a major challenge when using electronic instruments to measure things. Your task is to measure this voltage, despite the fact that it is noisy.
1. The Function Generator should be turned on and produces a noisy voltage when the NOISE button is pressed.
2. You can see a display of this voltage varying with time by using the AUTOSET button on the oscilloscope.
3. Set the timescale so that the time per division on the horizontal axis is 1 millisecond per division.
4. Use the MEASURE menu to display the MEAN of the voltage on CHANNEL 1.
5. Use the RUN/STOP button to take repeated measurements of the mean voltage.
6. Collect a sample of 25 measurements.
7. Do an analysis of these measurements (mean, standard deviation, uncertainty in the mean).
8. Make another 25 measurements and compare.

Exercise II: falling filters

1. Us a timer with at least 0.01 second precision to measure the time it takes for a coffee filter (oriented horizontally) to fall to the ground.
2. repeat this meaurement 10 times.
3. Do an analysis of these measurements (mean, standard deviation, uncertainty in the mean)
4. Make another 10 measurements with two filters stacked together and compare results.

1. Check that the Geiger counter is positioned 1 cm away from the source.
2. The number of particles hitting the Geiger tube can be measured using the RUN and STOP buttons on the Counter.
3. Use your timer and the Counter to make repeated measurements of the number of particles hitting the Geiger tube in 10 seconds.
4. Collect a sample of 25 measurements.
5. Do an analysis of these measurements (mean, standard deviation, uncertainty in the mean).
6. Make another 25 measurements and compare.

Group B Measurements (Do not take multiple samples)

Exercise IV: Total Internal Reflection

Measure the angle of incidence when the laser light ceases to be refracted through the surface and only reflects off of it (called total internal reflection. Note that because the beam has some width, you must judge the angle where the 'centre' of the beam is no longer transmitted. Make sure you are measuring the angle relative to normal incidence.

Exercise V:

Use a set of calipers to measure the diameter of three different hairs. Compare and comment on whether the calipers have enough resolution to see differences

Marking Scheme
3 marks for each group A measurement requires

complete all the measurements and describe how you did them (don't forget units)
perform data analysis
compare to a second set of data
identifying the dominant source of uncertainty, and suggest ways to improve the measurement.

Each Group B measurement is worth three marks, for which you are expected to:
make the measurement (diameter or angle), including an uncertainty estimate and describe how you did it (don't forget units).
make a comparison: another group in the case of internal reflectoin, different hairs in the caliper measurement.
identify the dominant source of uncertainty, and explain how this uncertainty could be reduced.