**See also (6)
**
More on
magnification and measuring the size of a cell using a graticule and stage
micrometer

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.
**

**A
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.
**

**An
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 10^{3}
=
25 000 µm (1 mm = 1 x 10^{3} 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 10^{3}
µm

Therefore
**image magnification** = image size / real image size =
35
x 10^{3}
/ 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 10^{3} = 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 10^{3}
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 10^{6}
µm

1 m
≡
1.0 x 10^{9} nm, 1 mm
≡
1.0 x 10^{3} µm, 1 cm
≡
1.0 x 10^{4} µm, 1 m
≡
1.0 x 10^{6} µm

(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 13/10^{6})

1 cm
≡ 10 mm
≡ 10 x 1 x 10^{3} = 1.0 x 10^{4}
µm, so diameter = 13
÷
10^{4} =
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 10**^{4}
nm

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