# A1-1: Measurements and Accuracy¶

## Apparatus¶

Microscope slide; vernier calipers; magnifying glass; micrometer; beam balance with masses; Archimedes’ bridge; beaker of water (\(250\text{ml}\)); metre ruler.

## Procedure¶

For each of the following, record the observations together with the possible error (i.e. ½ the smallest scale division), e.g.: \(46 \pm 0.5\text{mm}\). Calculate the mean value of repeated readings together with the error. Calculate the % error.

- Measure the slide thickness in a number of places using the metre ruler.
- Repeat using the vernier calipers instead.
- Measure the slide thickness in several places using the micrometer. For a mechanical micrometer, record the ‘zero reading’ and adjust the other readings correctly.
- Measure the length \(l\) and the width \(w\) using the metre ruler. Find the mass of the slide in air \(m\) , and then its apparent mass when suspended in water \(m_a\).

Then:

\[\begin{split}\text{upthrust} &= \text{weight of liquid displaced} \\
mg - m_a g &= \rho_w g \ \big(\text{slide volume}\big)\end{split}\]

where:

\[\begin{split}\text{slide volume} = \frac{m - m_a}{\rho_w} \\
\rho_w = \text{density of water}\end{split}\]

Then calculate the slide thickness \(d\) since:

\[l w d = \text{slide volume}\]

When you have completed the above, arrange the estimates of slide thickness in order (most accurate first).

Explain carefully why some methods are more accurate than others.