UK GCSE level age ~14-16, ~US grades 9-10 Biology revision notes re-edit 20/05/2023 [SEARCH]

Microscopy: 6. Examples of numerical calculations in microscopy, magnifying power of a microscope

Doc Brown's Biology exam study revision notes

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There are various sections to work through,

after 1 they can be read and studied in any order.

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(6) More on microscope magnification, measuring the size of a cell using a graticule & stage micrometer

See also (4) Examples of numerical calculations in microscopy - magnification and magnifying power of a microscope

As already mentioned, the size of structures is important in biological sciences.

Accurate measurements can be essential but even estimates can be good enough and quicker to obtain.

In Part 4. Ex 2. you were shown how to estimate the size of an onion cell - diagram below. I've reworked the diagram to give the idea of the circular field of view when observing a specimen under the microscope. Diagram of the microscope field of view of onion cells using a relatively high magnification.

Now cells tend to vary a little bit in size, so you would want an average value.

However, in the above field of view, there are only two cells across the diameter of the field of view giving a limited, and therefore less accurate, estimation of the average width of the onion cell.

The more cells you can clearly see and count in a row across the diameter of the field of view, the more accurate is your estimate cell size. A better image to estimate the size of an individual cell.

Average size of a single cell = diameter of field of view (d) divided by the number of cells (n) in a row across the diameter of the field of view.

In this case: average cell size = d / n = d / 9 (with appropriate length units)

Suppose the field of view of the above cells was ~0.20 mm, what would the average width of the cell be?

0.20 mm 0.20 x 10-3 m   2.0 x 10-4 m 2.0 x 10-4 / 10-6 = ~200 µm

average cell size = 200 / 9 = ~22 µm (2 sf)

Accurate measurement of cell size

In order to make accurate measurements of cell size you need to be able to calibrate the microscope.

Both the eyepiece and the field of view of the microscope stage need an accurate scale that can be focussed as well as the image of the specimen being examined under the microscope.

(i) The graticule

A graticule is a thin piece of glass/plastic onto which an accurate scale has been draw.

The graticule is positioned into the eyepiece of the microscope.

(ii) The stage micrometer

A stage micrometer is a microscope slide on which an accurate scale has been etched.

The stage micrometer is placed onto the microscope stage.

The microscope procedure using the graticule and micrometer

You place a stage micrometer on the stage of the microscope.

You line up one of the scale divisions of the eyepiece graticule with specific point on the stage micrometer.

You count the number of divisions on the eyepiece graticule that correspond with a specific measurement on stage micrometer.

You calculate the distance in micrometers of one division on the eyepiece graticule. Comparing the eyepiece graticule and stage micrometer scales

Diagram to show the positioning of the eyepiece graticule and stage micrometer scales in a microscope

You use the stage micrometer scale to calibrate the eyepiece graticule scale.

On the above diagram I've drawn two thin vertical lines to match up the scales of the eyepiece graticule and stage micrometer.

The stage micrometer is marked in 50 µm divisions.

The eyepiece graticule is marked as 100 arbitrary units (a.u.).

From the two vertical lines we can now calibrate the arbitrary graticule scale.

As you can see from the diagram: 64 - 35 = 29 a.u. ≡ 50 µm

Therefore each a.u. on the graticule scale = 50/29 = 1.72  µm

In this case the field of view is about 200 µm (0.20 mm)

Once the eyepiece graticule is calibrated, the stage micrometer can be removed from the stage and replaced with a specimen microscope slide for examination. How to use the eyepiece graticule scale to measure cell size.

Diagram showing the eyepiece graticule superimposed on the microscope specimen image.

From above we have a calibration of each a.u. on the graticule scale = 1.72 µm

Looking at the last diagram, the middle seven cells are measure from 7 to 90 a.u. on the graticule scale.

Therefore the average cell width is (90 - 7) / 7 = 11.87 a.u.

Using the conversion factor from above: average cell width = 11.86 x 1.72 = 6.96 = 20  µm (2 sf)

You can also pick out an individual cell and measure its size using the calibrated eyepiece graticule scale.

e.g. the 4th cell from the left: width = 43 - 30 = 13 a.u. on the graticule scale.

Therefore using the calibration factor: width of cell = 13 x 1.72 = 22 µm (2 sf)

Some other calculations based on the same cell diagram from above

(i) The diameter of the nucleus The nucleus is about 3 a.u. wide on the eyepiece graticule.

This equates to 3 x 1.72 = 5.1 µm  (2 sf)

OR you can make a less accurate visual estimate from the image.

On average the diameter of the nucleus is about a 1/4 of the diameter of the cell.

It looks as if the cell diameter equals about 4 diameters of the cell.

The average width of the cells was measured to be 20 µm

Therefore the average diameter of the nucleus is 20/4 = 5 µm  (1 sf)

(ii) The area of a cell

Most cells are roughly a square or rectangle in shape.

Suppose one of the cells in the diagram is 20 µm wide and 22 µm in length.

Area = length x width = 20 x 22 = 400 µm2

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