How do you calculate the magnification???????????????? Watch

Silent Assassin
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Hi im doing Biology AS with the OCR board. The topic on how to calculate magnification and what units to use, and all the relevant calculations really catch me out. Can anyone take me step by step how to do this, with an example. Any help would be much appreciated. A rep will also be given
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Tom H
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You should be provided with a scale in any scaled down diagram.

Hopefully it'll give a line and then the length it represents, for example a milimetre.

Measure that line with a ruler. Say it measured 1cm, which equals 10mm. Measured Size/Actual Size will give you your magnification. In this case, 10x.
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Silent Assassin
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Thanks for that. What about if it says calculate the actual size? what are all the unit conversions? e.g 1cm = 10mm, is there any others i need to know?
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Tom H
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If you wish to calculate the actual size you just rearrange the equation above.

Measured Size/Maginification = Actual Size

There is nothing wrong with keeping the same units as that of the measured size (unless the questions states otherwise). For example, if you measured something to be 1cm, and the magnification was 1000, the actual size can be expressed as 1/1000cm or 0.001cm.

This can in turn be converted to mm, um or nm.
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Abra
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Lets just say

magnification = m
actual size = a
picture size = X

To find the magnification you'd use X/a.
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sheena18
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ok - first thing don't panic!
i didn't understand it until like a week ago - and that was because i had mentally given up on it therefore i wasn't stressing about it.
so..

magnification is the number of times an image is compared with its real size

the equation for magnification = size of image/actual size

now here's some units and how to get from one unit to another:

1mm (millimetre) = 10^-3m
1 (micrometre - sorry i can't type it - its a funny 'u' then a 'm') = 10^-6m
1nm (nanometre) = 10^-9m
1A (angstrom) = 10^-10 m

So to get from millimetre to micrometre you multiply by 1000 - because millimetre is 10^-3m and micrometre is 10^-6m.
And to get from millimetre to nanometre you multiply by 1,000,000 (let me know if you can't see why)

The reason why we're multiplying by larger numbers each time is because the units are getting smaller and smaller - i.e. 1 centimetre is 10 tiny millimetres

Now lets go through an example for calculating magnification:

First draw out a roughish circle with a diameter of 30mm - this is gonna be a virus cell.
Now we're only told that its actual size is 200nm and we have to find magnification.

So first actually work out what these measurements are;
200nm - actual size (we're told that quite clearly)
30mm - this is the size of the image i.e. the picture of a virus cell - the one you can measure with a ruler

so we have an image size and an actual size so all we do is plug into the equation 30/200 right? - WRONG!!
*what you must never forget to do is ensure the units are the SAME*

so we'll make the 30mm into nm. looking at the units i've given above - it'll hopefully be clear to you that to get from mm to n you multiply by 1,000,000
so 30mm=30,000,000nm

now we can finally plug in magnification=image size/actual size
= 30,000,000/200
=15,000
so magnification is x15,000

To find something else e.g. actual size (you'll be given magnification and probably have to use a ruler to measure image size) all you do is rearrange the equation and plug in. so actual size=image size/magnification

Also go to this site and follow the animation to help you understand this topic:
http://www.cellsalive.com/howbig.htm

ok well i hope that helps - just let me know if u still don't understand!!
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Iscariot
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(Original post by sheena18)
1mm (millimetre) = 10^-3m
1 (micrometre - sorry i can't type it - its a funny 'u' then a 'm') = 10^-6m
1nm (nanometre) = 10^-9m
1A (angstrom) = 10^-10 m
1 millimetre (mm) = 10-3m
1 micrometer (µm) = 10-6m
1 nanometre (nm) = 10-9m
1 angstrom (A) = 10-10m

The micro sign is generally done using the Alt Gr key plus M, giving you a µ

The "to the power of" elevation in the text is done using the [sup] tags. Most people can never be bothered though since it's really time consuming to do it. Alternatively for writing things down here is done using the [sub] tags.

Interesting forum information for science/math forums.
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Revenged
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(Original post by Iscariot)
The micro sign is generally done using the Alt Gr key plus M, giving you a µ
I tried that in word and the computer didn't like it... :p:

Edit: All you have to do to work out magnification is divide the big number by the small one... I have no idea why some people think this is complicated!
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sheena18
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(Original post by Iscariot)
1 millimetre (mm) = 10-3m
1 micrometer (µm) = 10-6m
1 nanometre (nm) = 10-9m
1 angstrom (A) = 10-10m

The micro sign is generally done using the Alt Gr key plus M, giving you a µ

The "to the power of" elevation in the text is done using the [sup] tags. Most people can never be bothered though since it's really time consuming to do it. Alternatively for writing things down here is done using the [sub] tags.

Interesting forum information for science/math forums.
thanks for that iscariot - i've always wanted to know how u do that!
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Abra
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I can't find the Gr key!? where is it??
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sheena18
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(Original post by Abra)
I can't find the Gr key!? where is it??
its 'Alt Gr' - the first key to the right of the space bar! too funny!
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Silent Assassin
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Sheena: you are a legend! And thanks to all the other people, i understnd it properly now!
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Silent Assassin
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Quick question! In my test paper it gives us the actual size of 1.5µm. so how do i convert that to nm?
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JayEm
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(Original post by Silent Assassin)
Quick question! In my test paper it gives us the actual size of 1.5µm. so how do i convert that to nm?
Multiply by 1000
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Silent Assassin
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Ok here is a few examples i need help on:


1) The line AB in fig 3:1 represents an actual distance of 1.5µm.

calculate the magnification of the drawing.

( so in the diagram AB measures 1.2cm)

2) the actual thickness of the leaf along the line EF is 0.6mm.

calculate the magnification of the diagram

(the length of EF when i measured = 1.3cm)

3) the actual diameter of the nucleus, measured along the line XY is, 7µm.

calculate the magnification of the nucleas

(the length of XY = 4.4cm)





Now.... all the times, when i measured the lengths, they seemed pretty unusual measurments. I didn't understand. Like 4.4cm, 1.2cm..... etc. Can anyone please go through the answers with me, its so annoying i've been stuck with this flippin thing for 4 hours!!!!!!!!!!!!!!
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gyrase
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Remember cm = 10^-2m, µm = 10^-6m, mm = 10^-3m
(Original post by Silent Assassin)
1) The line AB in fig 3:1 represents an actual distance of 1.5µm.
calculate the magnification of the drawing.
( so in the diagram AB measures 1.2cm)
AB is represented by a length (1.2/10^2)m, when in reality it is (1.5/10^6)m, so the magnification is (1.2/10^2)/(1.5/10^6) = (1.2)/(1.5/10^4) = (1.2 x 10^4)/1.5 = 8000.
2) the actual thickness of the leaf along the line EF is 0.6mm.

calculate the magnification of the diagram

(the length of EF when i measured = 1.3cm)
EF is represented by a length (1.3/10^2)m, when in reality it is (0.6/10^3)m, so the magnification is (1.3/10^2)/(0.6/10^3) = (1.3)/(0.6/10) = (1.3 x 10)/1.5 = 22
3) the actual diameter of the nucleus, measured along the line XY is, 7µm.

calculate the magnification of the nucleas

(the length of XY = 4.4cm)
XY is represented by a length (4.4/10^2)m, when in reality it is (7/10^6)m, so the magnification is (4.4/10^2)/(7/10^6) = (4.4)/(7/10^4) = (4.4 x 10^4)/7 = 6286
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Silent Assassin
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Thanks very much, but the mark scheme gives some strange answers:

for the 2nd and 2rd examples:

2) award two marks if correct answer (50) is given
if measurement incorrect but in the range 25 –35 mm, allow one mark for a correct calculation
30/0.6 / 3(cm)/0.6(mm) / 3(cm)/0.06(cm) ; A +/- 1mm
50 ; A 48 - 52 R if units given


3) 7 cm / 70 mm or measurement / 7 m ; A 71 mm / 70 000 m
(magnification = x ) 10 000 ; A 10 143 NOT units (e.g. mm)


The parts highlighted in bold, are exactly from the mark schemes.
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Silent Assassin
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im riduclously confused with all the figures ;(;(;(;(. where did you get "when in reality it is (7/10^6)m"- where did 10 (to the power) of 6 come from
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Silent Assassin
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if possible could you put the figures from standard form into normal figures. Im not particularly good at maths, so i dont understand figures very well
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Revenged
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(Original post by Silent Assassin)
im riduclously confused with all the figures ;(;(;(;(. where did you get "when in reality it is (7/10^6)m"- where did 10 (to the power) of 6 come from
It is more normal to see 7x10^-6... but it is the same thing as 7/10^6 (7 divided by one million)
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