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(a) MICROSCOPES - use and development

 What is an optical light microscope? How is it constructed?

 How does a microscope work? How can we measure the size of a cell?

 What is the advantage of studying structures with a microscope?

 What do we mean by the resolution/resolving power of a microscope?

 What is the formula for magnification? How do you do magnification calculations?

What is the difference between a light microscope and an electron microscope? Which is the most powerful?

What do we use a microscope for in biology? and why is it such a useful investigative tool?

A microscope is an important instrument for studying cells e.g. the type of cell and the structure of cells.

Microscopes enable to see structures that we cannot see with the unaided naked eye.

Plant and animal cells can be studied in greater detail with a light microscope by magnifying the image.

Microscopes use a glass lens system to magnify images - with a bigger image you see more detail.

You can increase the resolution of an image by using more powerful and better quality lenses. Resolution means how good a microscope is at distinguishing between two points that are close together on an image. The higher the resolution the more clear is the image, especially when looking for fine details e.g. in a cell.

Microscopes enable you to see objects (like microorganisms) which you cannot see with the naked eye.

Microscopes using the visible part of the electromagnetic spectrum (visible light) were invented in the 16th century and the optical lens systems of light microscopes have been improved through the following centuries even until today.

With these microscopes, by passing light through a specimen up into a lens system, you can see individual cells and smaller details such as nuclei and mitochondria in all cells, and chloroplasts in plant cells.

Optical light microscopes

Light microscopes using visible light and lenses to form a magnified image of the object under investigation e.g. cells of plant or animal tissue. With a light microscope you can see individual cells and large subcellular structures like the nucleus, but not internal cell structures such as ribosomes or plasmids. The best light microscopes can give a magnification of 2000 times of a specimen's length.

The resulting image on a photographic plate, book or a computer screen is called a light micrograph.

Very high magnification is not possible with optical light microscopes. The limitation is due to the light gathering ability of the microscope and the short working distance of the lenses. This limits the total magnification of light microscope to about x 1500.

BUT, even with a high magnification, details may still not be that clear. The microscope must have a high resolving power - this is the resolution of the microscope. The resolving power is the smallest distance between two points that can be clearly distinguished. For optical light microscopes the best resolution is about 0.2 µm (200 nm).

However, unlike electron microscopes (described below), light telescopes can be used t observe living cells.

 

Electron microscopes - a means of looking at cells in more detail

Changes in microscope technology have enabled us to see cells with more clarity and detail than in the past, including simple magnification calculations.

Over time the design and usefulness of microscopes has improved, particularly using new technology in the 20th century and into the 21st century.

In the 20th century, with advances in atomic physics, the electron microscope (EM) was invented in the 1930s which uses beams of electrons instead of visible light photons. Electron microscopes use beams of electrons instead of beams of visible light photons. They have a much greater magnifying power and resolving power than optical light microscopes - larger sharper images.

So, using an electron microscope, using electrons instead of light photons, you can form images of very small subcellular structures such as ribosomes, plasmids and the internal structure of mitochondria (site of respiration) and chloroplasts (site of photosynthesis), because they have a much higher resolving power, but they are much more expensive!

Electron microscope images have a higher resolution than light microscopes - a higher resolving power increases the distinction between points on an image, i.e. you get a much sharper image of the fine detail of cell structure.

Electron microscopes can produce much greater magnified images (compared to light microscopes) of up to ten million (10⁹) times the real length of the specimen under investigation.

So electron microscopes are superior to optical light microscopes in terms of both magnification and resolution.

The resulting image on a photographic plate or a computer screen is called an electron micrograph.

Electrons do not form a colour spectrum, so all images are in black and white.

Electron microscopes can't be used to look at living cells - the electron beams would damage the function of living cells.

The transmission electron microscope (TEM) is particularly good at looking at very thin layers of biological materials e.g. a layer of cells and investigate in great detail the sub-cellular components of a cell e.g. plasmids and mitochondria and also viruses.

A transmission electron microscope is a large instrument, not very portable and very expensive. To prepare specimens for examination is a complicated process, and, unlike light microscopes, cannot be used to examine living tissue.

In a TEM, as the electron beam passes through the sample, some electrons are scattered and those that pass through are focussed by electromagnetic coils (instead of lenses) to produce an image on an electronic screen.

A TEM can examine very thin sections of cells up to a magnification of 10⁶ (million x) and with a resolution of less than 1 nm (10^-9 m). This is 200 x greater resolution than the best light microscopes.

The scanning electron microscope (SEM)

A scanning electron microscope works by bouncing beams of electrons off the surface of a specimen. The specimen must be first coated in an ultra-thin layer of a heavy metal like gold. The scattered electrons are again focussed by electromagnetic coils to produce an image on an electronic screen.

A SEM is used to produce images (micrographs) of the surface shape of structures of e.g. of individual cells or small organisms.

This has enabled the magnification produced by a microscope to be considerably increased to the point where you can see even smaller structures such as the internal detailed structure of mitochondria, chloroplasts and plasmids (hoops of DNA) so as to give a better understand of their structure and how their role in cell behaviour - in other words a powerful tool for better understanding how a cell works and the function of sub-cellular structures.

e.g. in animal cells or plant cells you can observe the fine detailed complex internal structure of important subcellular structures such as mitochondria (where aerobic respiration takes place), chloroplasts (where photosynthesis takes place), ribosomes (where protein synthesis takes place) as well as the detailed structure of specialised (differentiated) cells e.g. red blood cells (oxygen carriers) or white blood cells (immune defence system). In other words, electron microscopes allow more detailed studies of some pretty important structures and their functions!

Mitochondria and ribosomes can only be adequately viewed using an electron microscope and the 3D structure of biological specimens requires the use of an scanning electron microscope.

Extra note on microscopy methods

There is a technique called 'super-resolved fluorescence microscopy' which allows a much higher resolution than normal light microscopy. Since this is based on light, it means you can study living cells, which you can't do with electron microscopes - electron beams kill cells!

e.g. the size and shape of cells and subcellular structures are important, they are also variable, and such differences can be important e.g.

The complexity of mitochondria can indicate how active a cell is.

You can measure the ratio of the area-volume of the cytoplasm to that of the cell's nucleus.  A high ratio of cytoplasmic area-volume : nucleus area-volume can show a cell is about to divide. A low ratio can indicate a cancer cell.

 

You need to be able to use the following microscope formula:

For any microscope: magnification = length of image / real length of object, and for light microscopes:

total magnifying power = magnification of object lens x magnification of objective lens

and with a variety of units e.g. micro, nano etc. as well as expressing small numbers in standard form!

See Examples of numerical calculations in microscopy - magnification and magnifying power of a microscope

See also Introduction to plant and animal cell structure and function gcse biology revision notes

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(b) The design, function and use of an optical light microscope and slide preparation

Although scientists use the more powerful electron microscopes in research projects, many day-to-day investigations are performed using light microscopes. Examples include forensic science laboratories (e.g. evidence samples), hospital laboratories (e.g. examining the state/count of blood cells or looking for cancer cells by a pathologist).

The basic design of a light microscope

The basic design of an optical light microscope is shown in the left diagram. The back arch acts as a handle to carry the microscope around.

1. The eyepiece, through which you look at the image, is at the top of the tube that can move up and down when focussing the microscope. The eyepiece lens also magnifies the image produced by the objective lens.

2. There are two knobs for focussing - the course focussing knob is turned to get the image 'roughly' in focus and 'perfect' focus is enabled by turning the fine adjustment knob - moves in smaller increments on turning. The focussing knobs either move the stage or the eyepiece tube up or down to bring the image into focus.

3. On the stage, the prepared microscope slide (see below) is supported and held in place on the stage by clips - the slide needs to static to get good focus!

4. The lower end of the tube is connected to (usually) several objective lenses with different magnifications e.g. they might be marked X5, X10 or X20 etc. When at least two lenses are used it is referred to as a compound microscope.

5. The iris diaphragm under the stage controls the light intensity.

6. A mirror under the stage and iris directs a beam of light upwards through the stage, iris, slide and lens and up the tube to the eyepiece where you observe the image. You need a good bright light source to see any magnified image clearly.

Microscope slide preparation

The biological specimen you want to examine must be transparent, so you need a thin slice of it to let the light through.

To examine a specimen like plant or animal cells under a microscope you need to prepare microscope slide.

Live cells can be mounted in a drop of water or dilute sodium chloride salt solution (NaCl_(aq), saline).

Since most cells appear colourless you can apply a stain (dye) to give colour and enhance contrast.

You might use methylene blue to stain animal cells or iodine to stain plant cells (starch turns dark blue).

A microscope slide is a rectangular thin strip of glass or clear hard plastic onto which you mount the specimen.

You need a very thin slice of the material under examination, if it is too thick, the image is too complicated and likely to be blurred - so you may have thin out a thick specimen.

The specimen to be examined must be thin and transparent to visible light.

The most common specimen for first time use of a microscope are onion cells.

With a pipette you place a drop of pure water (or a special clear liquid called a mountant) onto the middle of a clean slide which helps keep the specimen in place.

Cut up an onion to separate it into layers and with tweezers peel off a thin strip of epidermal tissue and place it in the water on the slide.

Add a drop of dilute iodine solution to the water and onion cells.

The iodine solutions acts as a stain to highlight particular features of the specimen - the thin layers of onion cells.

If all of the sample is colourless you might not see much detail.

Different stains can be used to highlight different structures e.g.

Eosin dye is used to stain cytoplasm and methylene blue dye stains DNA.

Then place a cover slip over the specimen. A cover slip is a very thin square of glass or hard transparent plastic.

The cover slip should be placed on with great care and lowered into position so that no air bubbles are trapped underneath.

You can use a mounted needle to hold the cover slip up at an angle and slowly and carefully lower it onto the slide.

Press down gently making sure no air bubbles are trapped under the cover slip.

Air bubbles will either obscure or distort the image you are attempting to observe.

The microscope slide is now ready to be examined with the light microscope.

Using the microscope

Carefully clip the prepared slide onto the stage and make sure the specimen and cover slide are directly underneath the objective lens.

Initially use the less powerful objective lens to focus on the specimen, but first use the course adjustment knob to raise the stage to just below the objective lens.

It might be difficult to locate individual cells if you start off with too high a power lens, but a low power lens gives you an overall picture of the layout of the cells e.g. in human or plant tissue. It can also be easier to a cell count.

The circular area you see through the lens of a microscope is called the field of view.

With a very high powered lens the field of view is very small, almost at the level of few individual cells.

With a low power lens the field of view is much wider e.g. multiple cells of a thin slice of tissue.

Once you are focussed and made the appropriate observations and sketches, you can then increase the lens power to look for more detail.

Adjust the mirror and light source so the image seems bright, though not necessarily in focus yet.

Looking down the eyepiece, use the course adjustment knob to move the stage downwards until the image is roughly in focus.

Then use the fine adjustment knob to fully focus on the object and get a clear sharp image.

You then have the option of swapping to a higher powered objective lens to produce a more magnified image.

For scale measurements you can position a transparent ruler to measure the diameter of your field of view (FOV).

If you change to a more powerful objective lens for greater magnification you will reduce the FOV.

e.g. if you FOV was 10 mm and you swap to a lens that is five times more powerful your FOV is reduced from 10 mm to 10 ÷ 5 = 2 mm.

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(c) Drawing your observations - scale drawings

Give your drawing a title e.g. "Onion Cells" and quote the microscope magnification e.g. X50

You should record your observations as neatly and accurately as you can with a sharp pointed black pencil on white paper.

Make sure your sketch is a good size and cell walls with unbroken lines!

Don't use colouring or shading, just show the structures with neat thin lines.

Do you best to get the image features in proportion, either the adjacent cells of the layer or any subcellular structures you can see like the nucleus.

Carefully label the features of your drawing e.g. the cell features such as cell wall, nucleus, cytoplasm or chloroplasts, but not their very fine detailed structure.

Make sure your straight labelling lines match the label exactly!

See magnification calculations

Sketch - diagram of onion cells as seen under a microscope.

A scale bar has been marked on the drawing, allowing the size of a cell to be estimated.

I've just labelled the cell wall, nucleus and cytoplasm.

I've added a scale showing a length of 500 µm (500 micrometres, µ means 10^-6 in standard form).

The average size of an onion cell is ~200 µm, and the average size of the onion cell nucleus is ~6 µm.

The size of each cell and its nucleus do vary a bit from cell to cell.

 

How to work out a scale bar for your drawing by measuring the average real size of a cell

Note: In calculations I've used the symbol ≡ to indicate equivalence.

You fix a clear plastic ruler on the microscope slide and clip both of them onto the stage.

Select a magnification of at least X100 and refocus the microscope to obtain another clear image of the cells.

Adjust the slide so that the cells line up with the scale and count the number of cells along a line of 1 mm.

1 mm ≡ 10^-3 m (1/1000th of a metre).

A micrometre is 1 millionth of a metre, 1.0 x 10^-6 m (in standard form).

Therefore 1 mm ≡ 10^-3/10^-6 = 1000 µm

Suppose the length of 5 onion cells = 1 mm, average length 0.2 mm.

1 mm ≡ 1000 µm, so the average length of one onion cell = 1000/5 = 200 µm

Once you know the average length of one cell you can use it to calculate the length of the scale bar on you diagram using the formula below. Suppose you want a 500 µm scale bar on your drawing.

scale bar length (for 500 µm) = 500 x drawing length of cell (µm) ÷ actual length of cell (µm)

e.g suppose each cell you have drawn was on average 2.0 cm long on paper.

This is 20 mm, which equals 20 x 1000 = 20,000 µm and the actual real average length is 200 µm

scale bar length = 500 x 20,000 ÷ 200 = 50,000 µm

50,000 ÷ 1000 = 50, so the scale bar on my drawing would be 50 mm or 5 cm long.

 

AND you can calculate the actual magnification of your drawing compared to the specimen's real size.

The magnification of your drawing = average length of drawn cell (µm) ÷ average real length of cell (µm)

The drawn cell is 20 mm long ≡ 20 x 1000 = 20,000 µm, real length of cell is 200 µm

magnification of drawing = 20,000 ÷ 200 = 100X

 

For more on estimating cell size see More on magnification & measuring the size of a cell using a graticule & stage micrometer

 

Other microscope drawings

e.g. on the left a typical plant cell x 200 to x 500 magnification.

Note that is a simple black and white line drawing.

See magnification calculations

See also

Introduction to plant and animal cell structure and function gcse biology revision notes

 

Other examples of what you can see with a powerful light microscope

Cell division - mitosis

You can stain chromosomes so that they are made visible under a microscope using a 'squashed' layer of cells under the cover slip.

This enables you to actually visually follow the stages of mitosis.

In the school laboratory you can use cells from a plant root tip (e.g. garlic cloves) to observe the various stages of the cell cycle.

A few drops of the stain (dye molecule solution) is added to the plant tissue sample and the mixture squashed on the microscope slide so that you can see the chromosomes more easily.

You can clearly observe the chromosomes being pulled apart in a cell and the subsequent formation of two cells as the mitosis cell division proceeds - fascinating viewing.

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(d) Examples of numerical calculations in microscopy - magnifying power of a microscope

Calculations involving scale drawings and magnification I've dealt with above.

Note: In these exemplar calculations I've used the symbol ≡ to indicate equivalence.

You need to be able to use the prefixes centi (10^-2), milli (10^-3), micro (10^-6) and nano (10^-9) and express answers in standard form when carrying out calculations involving magnification, real size and image size using the magnification formula (below).

The reason for this is that that the real size of the objects under investigation with a microscope are very small!

Magnification formulae

Magnification of image

e.g. solving magnification problems and the relative sizes of object e.g. a cell and its observed image in a microscope.

The formula 'triangle' for magnification is shown on the right (size = length).

When using the formula: magnification of image = the image size ÷ object size

make sure the image size and object size are in the same length units!

Rearrangements: image size = magnification x object (specimen) size

and the real object size = image size ÷ magnification

Note: The quoted magnification of image in a textbook is quite valid and important. However the same cannot be said for the image on a computer screen. The screen resolution might be different from one screen to another, even for the same original image, so the magnification will appear to be different.

Two examples of calculations of image size magnification

I'm just using two previously used cell diagrams.

Ex 1. plant cell calculation of magnification of image

From the microscope scale the real width of the plant cell is 0.10 mm.

On a paper printout, the width of the plant cell is 15 mm.

image magnification = image size / actual real size of object = 15 / 0.10 = 150

 

Ex 2. onion cell calculation

From the microscope scale, two of the onion cells have on average a real total length of ~400 µm.

So the real cell length is ~200 µm

On a  paper printout, the length of two cells on average is ~5.0 cm,.

So the image cell length = ~2.5 cm

You must convert one of the numbers, so that both numbers have the same units.

2.5 cm ≡ 25 mm ≡ 25 x 10³  = 25 000 µm (1 mm = 1 x 10³ µm)

Image magnification = size of image / size of object = 25 000 / 200 = 125x

Ex 3. A micrograph

A micrograph of a red blood cell is 35 mm long.

If the red blood cell has a diameter of 7.0  µm, what is the image magnification?

You first need to do a unit conversion: 35 mm ≡ 35 x 10³ µm

Therefore image magnification = image size / real image size = 35 x 10³ / 7.0 = 5000

 

Total magnification of microscope - do NOT confuse with the above 'image magnification'

If you know (and you should!) know the magnifying power (x...) of both the eyepiece lens and the objective lens, it is quite easy to calculate the total magnifying power of the microscope.

The following simple formula for magnification is:

total magnification = eyepiece lens magnifying power x objective lens magnifying power

e.g. if the eyepiece lens power is x 5 and the objective lens power is x 50, the total magnification is 5 x 50 = x250

Simple rearrangement allows you to calculate the magnification necessary for a particular lens for a specified total magnification.

e.g. If an eyepiece lens has a magnification of 20x, what must the magnification of the objective lens (z) be to give a total magnification of 800x?

total magnification = 800 = 20 x z

z = magnification of the objective lens = 800 / 20 = 40x

And: If an objective lens has a magnification of 30x, what must the magnification of the eyepiece lens (y) be to give a total magnification of 1500x?

total magnification = 1500 = y x 30

y = magnification of eyepiece lens is 1500 / 30 = 50x

Further note on units

metres (m), centimetres (1 cm ≡ 1.0 x 10^-2 m), millimetres (1 mm ≡ 1.0 x 10^-3 m)

micrometres (1 µm ≡ 1.0 x 10^-6 m), nanometres (1 nm ≡ 1.0 x 10^-9 m)

See the questions below for other examples of unit conversions and presenting lengths in standard form.

 

Examples of microscope scale calculations

BUT, first a note on conversion factors for length

With the naked eye you can see (resolve) objects of width ~0.04 mm (0.04 x 10³ = 40 µm)..

Most animal and plant cells are ~0.01 to 0.1 mm in 'diameter' (10 to 100 µm), so some can be seen with the naked eye, but most can only be resolved, that is clearly observed, using a microscope.

Most cell dimensions e.g. diameter of cell are measured in micrometers (µm, 10^-6 m), but the size of even smaller  subcellular structure or viruses are often measured in the smaller unit nanometre (nm, 10^-9 m)

You need to be able to use lots of equivalents - length conversion factors e.g.

based on nanometre nm, micrometre µm, millimetre mm, centimetre cm, metre m length units

1 mm ≡ 0.1 cm ≡ 1/1000 m = 0.001 m = 1.0 x 10^-3 m ≡ 1000 or 1 x 10³  µm

1 µm ≡ 1/1000 mm ≡ 1.0 x 10^-3 mm ≡ 1 x 10^-6 m ≡ 1000 nm (1 nm = 1.0 x 10^-9)

1 nm ≡ 1/1000 µm = 0.001 µm = 1.0 x 10^-3 µm

1 µm ≡ 10^-6 m, 1 nm ≡ 1.0 x 10^-9 m, 1 cm ≡ 1.0 x 10^-2 m, 1 m ≡ 1.0 x 10⁶ µm

1 m ≡ 1.0 x 10⁹ nm, 1 mm ≡ 1.0 x 10³ µm, 1 cm ≡ 1.0 x 10⁴ µm, 1 m ≡ 1.0 x 10⁶ µm

etc. etc.!

(You need to use the above for scale conversions to solve the problems given below)

 

Q1 A white blood cell has a diameter of 13.0 µm (13 micrometres)

Express the diameter of the white blood cell in various units...

13.0 µm ≡ 13 x 1.0 x 10^-6 m = 1.3 x 10^-5 m  (you get the same answer from 13/10⁶)

1 cm ≡ 10 mm ≡ 10 x 1 x 10³ = 1.0 x 10⁴ µm, so diameter = 13 ÷ 10⁴ = 1.3 x 10^-3 cm

1 mm ≡ 1000 µm, so 13 µm ≡ 13 ÷ 1000 = 0.013 mm = 1.3 x 10^-2 mm

1 µm ≡ 1000 nm, so 13.0 µm ≡ 13  x 1000 = 13,000 = 1.3 x 10⁴ nm

Just try working them out in your own way and see if you agree with my answers

 

Q2 A red blood cell has a diameter of 0.012 mm.

Give the red blood cell diameter in metres, millimetres, micrometres and nanometres all written in standard form.

0.012 ÷ 1000 = 1.2 x 10^-5 m  (1 m  ≡ 1000 mm)

0.012 mm = 1.2 x 10^-2 mm  (just changed to standard form)

0.012 mm ≡ 0.012 x 1000 = 1.2 x 10¹ µm  (1 mm  ≡ 1000 µm)

0.012 mm ≡ 0.012 ÷ 1000 = 1.2 x 10^-5 m, 1.2 x 10^-5 ÷ 10^-9 = 1.2 x 10⁴ nm  (1 m  ≡ 1000 m, 1 m  ≡ 10⁹ nm)

Again, just try working them out in your own way and see if you agree with my answers

 

Q3 Suppose the real length of a cell is 150 µm.

What is the size of the cell image with a microscope magnification of X 50? (give you answer in µm and mm)

image size = magnification x object size, 1 mm ≡ 1000 µm

image size = 50 x 150 = 7500 µm and 7500 ÷ 1000 = 7.5 mm

 

Q4 The image of a red blood cell is 7.0 mm under a microscope magnification of 1000 X.

What is the real size of the red blood cell? (give your answer in micrometres and nanometres)

1 mm ≡ 1000 µm, so 7.0 mm ≡ 7.0 x 1000 = 7000 µm.

object size = image size ÷ magnification

real object size = 7000 ÷ 1000 = 7.0 µm

1 µm ≡ 1 x 10^-6 m, 1 nm ≡ 1 x 10^-9 m, so 1 µm ≡ 10^-6 ÷ 10^-9 = 1000 nm

Therefore cell diameter = 7.0 x 1000 = 7.0 x 10³ nm

 

Q5 What magnification is needed to produce a 10 mm image of a cell from a specimen cell of diameter 125 µm?

magnification = image size ÷ actual size

1 mm ≡ 1000 µm, so 10 mm ≡ 10,000 µm

magnification needed = 10,000 ÷ 125 = 80 X

 

Q6 If a cell has diameter of 0.000090 m what is its diameter in ...

(a) standard form?

move the decimal place 5 place to the right and multiply the answer by x 10^-5 giving 9.0 x 10^-5 m

(b) micrometres (µm)?

1 µm = 10^-6 m, so move the decimal point forward 6 places to give 90 µm

 

Q7 A specimen is 60 µm wide.

Calculate the width of the image in mm under a magnification of x200.

image size = magnification x real size

image size = 200 x 60 = 12000 µm

1000 µm = 1 mm (1 µm = 1 x 10^-6 m, 1 mm = 1 x 10^-3 m, 10^-3/10^-6 = 1000)

12000/1000 = 12 mm

 

Q8 A cell is 3 x 10^-5 m wide.

Calculate the width of the image under a microscope magnification of x 200.

Quote you answer in (a) metres and (b) micrometers, written in standard form.

image size = magnification x real object size

(a) image size = 200 x 3 x 10^-5 = 600 x 10^-5 = 6.0 x 10^-3 m

(b) Since 1 µm ≡ 1.0 x 10^-6 m, micrometers = metres x 10⁶

therefore image size = 6.0 x 10^-3 x 10⁶ = 6.0 x 10³ µm

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(e) The scale of things and orders of magnitude

 When comparing the size of small objects like cells, scientists refer to differences in sizes as an order of magnitude.

This means that an object is described as being greater of smaller by a factor of 10.

For example, the leaf cell size is one order (10 x) in size than a red blood cell.

The common ladybird is two orders greater (100 x or 10 x 10) in size than a plant leaf cell.

The thickness of the cell membrane is three orders smaller {1/1000 or 1/(10 x 10 x10)} than the diameter of a red blood cell.

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

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 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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aqa gcse 9-1 biology: You should be able to: understand how microscopy techniques have developed over time, explain how electron microscopy has increased understanding of sub-cellular structures, and appreciate the differences in magnification and resolution that have both increased with technological development in microscopy. Know and understand that an electron microscope has much higher magnification and resolving power than a light microscope. This means that it can be used to study cells in much finer detail. This has enabled biologists to see and understand many more sub-cellular structures. You should appreciate the differences in magnification and resolution between a light microscope and an electron microscope. Be able to explain how electron microscopy has increased understanding of subcellular structures. Be able to use prefixes centi (10^-2), milli (10^-3), micro (10^-6) and nano (10^-9) (expressing answers in standard form) and carry out calculations involving magnification, real size and image size using the formula: magnification = size of image / size of real object . With light microscopes you can see individual cells and large subcellular structures like the nucleus. With electron microscopes, using a beam of electrons instead of a beam of light, you gain a much higher resolution seeing much smaller objects e.g. the structures of mitochondria, chloroplasts, ribosomes and plasmids.