# 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.

1. Measure the slide thickness in a number of places using the metre ruler.
2. Repeat using the vernier calipers instead.
3. Measure the slide thickness in several places using the micrometer. For a mechanical micrometer, record the ‘zero reading’ and adjust the other readings correctly.
4. 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.