Using a microscope to measure cell size

Cell size can be measured using an eyepiece graticule. The graticule has a ruler on it.

You must find out the distance measured for each division of the graticule. You can then use the graticule to measure cells. The distance will be different for each objective lens of the microscope.

To do this, you will use a stage micrometer. You will use this to calibrate the eyepiece graticule. Once it's calibrated the same measurements can be used each time you use the microscope.

Cell size can be measured using an eyepiece.
  • Place a stage micrometer on the stage of the microscope.
  • Line up one of the divisions on the eyepiece graticule with a fixed point on the stage micrometer.
  • Count the number of divisions on the eyepiece graticule that correspond with a set measurement on the stage micrometer.
  • Calculate the distance in micrometres of one division on the eyepiece graticule.

The distance of 250 μm on the stage micrometer lines up against divisions at 10 and 61 on the eyepiece graticule.

61 - 10 = 51 divisions on the eyepiece graticule are equivalent to 250 μm on the stage micrometer.

One division on the eyepiece graticule is equivalent to μm on the stage micrometer:

= 4.9 μm (to two significant figures).

Therefore one graticule division is equal to 4.9 μm.

Using the same calibrated eyepiece graticule to measure a cell:

The calibrated eyepiece graticule can be used to make measurements of any cells or other structures viewed with the microscope on that magnification

The calibrated eyepiece graticule can be used to make measurement of any cells or other structures viewed with the microscope on that magnification.

The width of the cell highlighted = 52 - 40 = 12 eyepiece graticule divisions.

The real width of the cell is 12 × 4.9 μm = 59 μm (to two significant figures).

Question

What would be the length of a plant cell, to two significant figures, that was 35 divisions on this graticule?

170 μm.

Each eyepiece graticule division is 4.9 μm.

The real width of the cell is 35 × 4.9 μm = 171.5 μm,

To two significant figures, this is 170 μm.

Question

How many graticule divisions would a single celled organism that was 240 μm take up?

49

Each graticule division is 4.9 μm.

An organism that measured 240 μm would take up  \frac{240}{4.9} divisions = 49 divisions.

0.1=  \frac{1}{10}= 10-1
0.01=  \frac{1}{100}= 10-2
0.001=  \frac{1}{1000}= 10-3

If you increase a number by one order of magnitude, you are multiplying the number by 10.

If you decrease a number by one order of magnitude, you are dividing the number by 10, which is equivalent to multiplying by 0.1.

For instance, a 2 m tall person and a 20 m tall oak tree differ by one order of magnitude.

The person's height = 2 m = 2 × 100 m

The oak tree's height = 20 m = 2 × 101 m

Hence there is one order of magnitude between the height of a human being (2 m) and the height of an oak tree (20 m).

Notice that when dividing numbers in standard form, we subtract the powers.

When comparing orders of magnitude, actual distances can be approximated. It's the relative difference that is important.

Question

What is the difference in order of magnitude between a human hair and HIV?

The width of a human hair is 100 μm, while the width of the HIV is 100 nm.

The difference in order of magnitude is 3.

Calculation:

The width of the human hair is 100 μm = 10-4 m.

The width of the HIV is 100 nm = 10-7 m.

So, there are three orders of magnitude difference:

 \frac{10 - 4}{10 - 7} = 3.

Or, more simply:

4 - (-7) = -4 + 7 = 3.

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