Magnification Help

[Laurens]

I have a bit of homework that is puzzling me. There is a sheet of illustrations of cells etc, and I have to try and work out the magnification from their apparent and actual size. I have been stumped a little bit, because in one image the scale at the bottom for 0.01mm is 31mm long, yet the apparent size of the cell is 24mm, my maths is terrible and I have no idea how to translate this into its actual size when the scale is bigger than the apparent size of the image...

 

I hope that makes sense. I'll try to clarify if it's not clear.

 

Much appreciated

Laurens

[John Cuthber]

" I have no idea how to translate this into its actual size when the scale is bigger than the apparent size of the image"

What would you do if it was smaller?

[Laurens]

If it was smaller I would see how many times that scale would fit into the image.

 

For example, if the scale for 0.01mm was 10mm long, and the cell in the image was 40mm long then it would be 0.04mm

 

But I'm still not sure how it would work the other way around, especially not in this example...

[John Cuthber]

0.04 is 40/10 times 0.01

[michel123456]

(...) in one image the scale at the bottom for 0.01mm is 31mm long,

 

That means 31 mm on your image represents 0,01mm in reality.

 

 

yet the apparent size of the cell is 24mm, (...)

 

So 24mm on your image represents .... in reality.

Edited September 18, 2011 by michel123456

[Hal.]

Is it the magnification in one dimension or in two dimensions that is needed , if I see this correctly ?

 

Case 1 .

 

If there was a picture which was 100 mm wide magnified and it represented 5 mm actual width

then the magnification of the width would be 100 mm / 5 mm = 20

 

If the magnification of the area was of interest then this would be the product of the magnifications of the width and the length , thus 20 x 20 = 400

 

Case 2 .

 

If there was a picture which was 1000 mm wide magnified and it represented 200 mm actual width

then the magnification of the width would be 1000 mm / 200 mm = 5

 

If the magnification of the area was of interest then this would be the product of the magnifications of the width and the length , thus 5 x 5 = 25

 

Case 3 .

 

If there was an image which was 50 mm wide magnified and it represented an actual width of 0.001 mm

then the magnification of the width would be 50 mm / 0.001 mm = 50 000

 

The magnification of the area would be 50 000 x 50 000 = 2 500 000 000

[Laurens]

I'm sorry if I'm being slow, or missing something really obvious.

 

I know how I'd work out the magnification from the apparent size/actual size. The thing that is puzzling me is working out the actual size when the scale is larger than the apparent size of the image.

 

If the scale is 31mm long, representing 0.01mm, yet the apparent size of the image is 24mm long - this is 5mm shorter than the length of the scale - I just can't work out how to work that translates to in terms of the actual size.

 

I know the actual size must be shorter than 0.01mm I'm just having trouble working out how much shorter. Am I making sense?

[Hal.]

If 40 mm represented 0.5 mm , then 30 mm would represent 30 mm / 40 mm of 0.5 mm = 0.75 x 0.5 mm = ?

 

If 31 mm represented 0.01 mm , then 24 mm would represent 24 mm / 31 mm of 0.01 mm = ?

[michel123456]

 

I know the actual size must be shorter than 0.01mm I'm just having trouble working out how much shorter. Am I making sense?

 

Yes. You are correct.

 

How much shorter?

 

You must use math.

 

When 31 mm represent 0,01 mm, how much represents 24 mm?

The result is a fraction of 0,01mm.

You know what a fraction is, I suppose.

You have 2 numbers to use in order to make this fraction, 31mm and 24 mm.

One way will give you MORE than unity, the other way will give you LESS than 1. (that's the good one)

Multiply the result of the fraction by 0,01mm, and bingo!

I cannot help further without giving the numerical answer.

 

----------

whoops, Hal answered first.

 

_____________-

@Hal.

scales are always linear by convention. I am not aware of any other way to express scaling.

Edited September 19, 2011 by michel123456

[Hal.]

Michel ,

 

If width dimension is at 100 : 1 and breadth dimension is at 100 : 1 then the scale of area is at 10 000 : 1

 

This is a derived scale of area from the overall scale and on a technical drawing the scale given would be , all dimensions 100 : 1

[Laurens]

Got it now, thanks guys

[Hal.]

Laurens ,

 

When people use smaller dimensions such as 0.500 mm this is called 500 microns , 1 micron is 1 millionth of a Metre

 

0.007 mm would be 7 microns

 

0.008 mm would be 8 microns

 

0.007 742 mm would be 7.742 microns to 3 decimal places

[michel123456]

Michel ,

 

If width dimension is at 100 : 1 and breadth dimension is at 100 : 1 then the scale of area is at 10 000 : 1

 

This is a derived scale of area from the overall scale and on a technical drawing the scale given would be , all dimensions 100 : 1

 

Correct.

 

You may also encounter technical drawings where scale along X is different from scale along Y.

[Laurens]

We went through it in class today, it turns out I didn't actually have to answer the question that I was struggling with! (Which might explain a lot) - I have got to grips with it now though. Thanks for the help people