MICROSCOPY - the scientific uses of microscopes in biology
Light and electron microscopes - preparation of samples for investigation e.g.
slides and how to estimate the size of a cell and its features e.g. size of
nucleus
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school biology revision notes: GCSE biology, IGCSE biology, O level
biology, ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old
students of biology.
Some
of these revision notes on how to use a microscope, making up a side
ready for study, how to make labelled drawings from your observations
and learning how to calculate magnification and the advantage of
electron microscopes over optical light microscopes are suitable for UK KS3 Science-Biology
(~US grades 6-8).
Sub-index for this page on microscopy
(a)
Microscopes -
use and development
(b)
The design,
function and use of an optical microscope and slide preparation
(c)
Drawing your
microscope slide observations - scale drawings
(d)
Examples of
numerical calculations in microscopy - magnification and magnifying power of
a microscope
(e)
The scale of things
and orders of magnitude - comparison of cells and other objects
(f)
More on
magnification and measuring the size of a cell using a graticule and stage
micrometer
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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
TOP OF PAGE
for SUB-INDEX
(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.
TOP OF PAGE
for SUB-INDEX
(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.
TOP OF PAGE
for SUB-INDEX
(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
TOP OF PAGE
for SUB-INDEX
(e) The
scale of things and orders of magnitude
Object |
Size |
|
Object |
Size |
a common
ladybird |
~7 mm, 7000
µm |
|
HIV virus |
~0.1
µm,
~100 nm |
diameter of a
human hair |
~0.1 mm, ~100
µm |
|
thickness of
cell membrane |
~0.007
µm, ~7 nm |
typical plant
leaf cell |
~0.07 mm, ~70
µm |
|
diameter of
DNA strand |
~2.5 nm |
diameter of
red blood cell |
~0.007 mm, ~7
µm, 7000 nm |
|
diameter of a
carbon atom |
~0.34 nm |
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.
TOP OF PAGE
for SUB-INDEX
(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
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.
IGCSE revision
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