ngc1514 Loc: Atlanta, Ga., Lancaster, Oh. and Stuart, Fl.

The 0 in 2010 in a penny's date. Gauging by eye with a metric ruler, the 0 looks to be about 1mm high. On my computer screen, it shows up about 165mm.

http://ericpix.net/Online/Hog/penny_1.jpg

Nikonian72 Loc: Chico CA

If this image is full sensor (uncropped), the "0" occupies about 5/7 of 24-mm high sensor = 17-mm. Original is 1-mm, so (17x long) x (17x wide) = 289x magnification.

Yikes! This is Photo-Micrography. What lens set-up?

English_Wolf Loc: Near Pensacola, FL

*ahem*
Magnification = Size of image / Actual size
289 = x / 1 (mm)???
x on monitor (blown up from sensor or 1:1?) = 165 mm
so

y = 165 / 1 = 165x, not 289... and on monitor...
on full sensor the max size is
Y = 36 / 1 = 36x
Magnification from sensor to monitor
165 / 36 = 4.6x

We are far from 289x... Where did you get this magnification formula from???

Nikonian72 Loc: Chico CA

Size on monitor (or print) has nothing to do with magnification capture. You can print this image to the size of a building, but the captured magnification does not change.

It is simple math, having nothing to do with the number 165. As stated above: the "0" measures about 5/7 of 24-mm high sensor (actual D300 size = 23.6-mm x 15.8-mm), which equals about 17-mm high on sensor. Do you dispute this?


Original is 1-mm high, so captured image is 17x as long, AND 17x as wide. Do you dispute this?

(17x long) x (17x wide) = 289x magnification.

ngc1514 Loc: Atlanta, Ga., Lancaster, Oh. and Stuart, Fl.

Here's the setup. It's an Amscope compound trinocular microscope with the D300 plugged into the camera port and tethered to a computer. For only $280 the microscope is a LOT cheaper than many lenses and a lot of fun to play with.

http://ericpix.net/Online/Hog/microscope.jpg

English_Wolf Loc: Near Pensacola, FL

I dispute the use of x*x as in this case this is a surface.

If you use magnification = size of image on sensor / actual size you need to select one dimension or another or a surface on BOTH sides of the equation.

Nikonian72 Loc: Chico CA

This is NOT a one dimensional magnification. Not only did it elongate, but it widened as well. Two dimensions equal x * y. BOTH directions expanded 17x, so 17 * 17 = 289 magnification.

Nikonian72 Loc: Chico CA

Did you use the basically the same camera/lens set-up for your penny photo (reflected light) as the pollen photo (transmitted light)?

ngc1514 Loc: Atlanta, Ga., Lancaster, Oh. and Stuart, Fl.

No, I was using a 10x objective for the pollen and a 4x objective for the penny. As you noted, the penny was shot with reflected light while the pollen transmitted. I need to get a microscope scale to measure actual magnification with each objective.

I've been messing around with optics for a long time and have to agree with English Wolf. While Galileo talked about his early telescopes enlarging objects by 900 times, the scope was actually a 30 power instrument. He did the same squaring you are, but that's never used in astronomy or, as far as I know, microscopy. Magnification is a unitless measurement and squaring the magnification is not useful. Yes, the "0" is taking up more AREA, but so is the moon when I slap a 100x eyepiece on the scope. But I don't say I have magnified it 10,000 times.

English_Wolf Loc: Near Pensacola, FL

The problem lies into your understanding of the situation. Magnification is calculated according to a linear formula.

You are looking at an area so, for you 2x = 4 in area when in reality it is just that 2x. 2x refers to a distance, as "I was half way to the moon when I took this picture (2x visual effect)" of course you will see more details into a seemingly larger area that is 4x wider, same goes for photography.

The funny part is, when you arrive to extremes, you realize that you see less (in area), not more, by a factor equal to the magnification. You just see more details.

This can be illustrated by the scale of a map. The more detailed, the smaller the mapped area, check google maps/earth to see this at work.
----
In astro-photograpy this is critical as the more magnified an object the faster it moves across the viewing field*. Same effect as the horizon being slow to move when viewed from a car window and the road edge appears to be faster, just reversed. A tree at the side of the road will 'move' at 55mph relative to car. Another tree on the horizon will 'move' faster** but appear slower...

* East to West? Earth rotates toward the East and moves toward the west... The sun is relatively static compared to Earth point of view (I know corkscrew motion wobble and all that). It rises on the East and sets in the west... Man, I am getting old.
** triangulation effect. This is not true if you drive in wide circle around a distant object, at which point it will 'move' in angular fashion. Now we get into physics, geometry and it becomes boring.

ngc1514 Loc: Atlanta, Ga., Lancaster, Oh. and Stuart, Fl.

Taking it down to the practical... the magnification of a telescope is calculated by dividing the focal length of the primary optic by the focal length of the eyepiece. My 16" scope has a 72" focal length, so if I drop a 1" f/l eyepiece in it, I get 72x. A .5" f/l eyepiece gives me 144x and so on.

Yes, if I move from a 4x5 camera to an 8x10, the area of the negative is increased by 4, but the size (a linear measurement) is doubled. The size is how we measure magnification.

Nikonian72 Loc: Chico CA

The major mistake in this reasoning is that linear magnification is fine for 1-dimensional measuring between point "A" and point "B", but not for 2-dimensional measuring of an area, where height is increased by same rate as width (distance). Cameras record area, not distance.

For sake of this illustration, please consider image #1 to be 1:1 (life-size). Image is 4 tiles wide by 4 tiles high = 16 tiles.

If we move in 1/2 the distance, we view half the width (2 tiles) and half the height (2 tiles). Image #2 is now 2 tiles by 2 tiles = 4 tiles = 1/4 area of image #1 = 4:1 magnification (4x life-size).

If we again move in 1/2 the distance (1/4 of original), we view half the width (1 tile) & half the height (1 tile) of image #2. Image #3 is now 1/4 area of image #2, and 1/16 area of image #1 = 16:1 magnification (16x life-size).

The single tile in image #3 is 16x the size of any tile in image #1.

16 tiles represents 1:1 (life-size)


4 tiles represent 4:1 magnification (1/4 area of image #1)


1 tile represents 16:1 magnification (1/4 of image #2, and 1/16 of image #1)

ngc1514 Loc: Atlanta, Ga., Lancaster, Oh. and Stuart, Fl.

Douglass,

You are trying to change the definition of "magnification." Magnification is a linear, dimensionless quantity according to any book on optics you care the check. In no definition I am aware of is the multiplication of length and width used in calculating the magnifying power of an optical system.

You have provided a useful example of the inverse square relationship, but it is not how magnification is defined in science.

Starting with Wiki on Magnification:

Photography: The image recorded by a photographic film or image sensor is always a real image and is usually inverted. When measuring the height of an inverted image using the cartesian sign convention (where the x-axis is the optical axis) the value for hi will be negative, and as a result M will also be negative. However, the traditional sign convention used in photography is "real is positive, virtual is negative".[1] Therefore in photography: Object height and distance are always real and positive. When the focal length is positive the image's height, distance and magnification are real and positive. Only if the focal length is negative, the image's height, distance and magnification are virtual and negative. Therefore the photographic magnification formulae are traditionally presented as:

M = {di \do} = {hi \ho} = {f \do-f} = {di-f \f}

The symbols are presented in this diagram:

http://upload.wikimedia.org/wikipedia/en/thumb/e/ee/Basic_optic_geometry.png/220px-Basic_optic_geometry.png

Moving to Basu's Dictionary of Pure and Applied Physics:

The magnification of an optical system indicates the effectiveness of enlarging or reducing an image. There are several kinds of magnification: lateral magnification of an image, axial magnification of an image or magnification of the magnifying power of an optical instrument. It is important which magnification should be considered for use to treat optical magnification. The term magnification is sometimes used simply to mean lateral magnification of a lens without qualification.

Basu continues with the formulae to calculate each type of magnification. In no instance is the height and width of the magnified object multiplied in the calculation.

I agree with everything you say, but you are NOT defining magnification of an optical system. Enlarge is not a term defined in Basu's Dictionary nor does it give a true indication of the performance of an optical system. If I tell someone my 1600x microscope enlarged 2.56 million times, no one is going to believe it unless it's an electron microscope.

I expect most of us think lateral magnification and not the multiplication of the lateral mag of the height and width of the image formed by an optical system. It's the same working the other direction on the focal length range. If a 50mm lens is "normal", a 500mm will magnify the image 10 times when compared to the normal lens. Yes, the tile you used will cover a 100x greater area, but that ain't magnification.

Whew...

Viceroy

This is all fascinating information, even though I am genuinely lost. You guys are absolute scientists. I will now have to tell my wife I am taking a physics class for my macro photography. :thumbup:

Nikonian72 Loc: Chico CA

I am NOT changing the definition of "magnifying power". I have previously read all of the literature you cited, and much more. I know you found, as I did, references where area magnification was questioned by others. Convention dictates term usage, not always logic.

As an example, a 2x power lens will increase area 4x. When I label an insect as 4x life-size, I do not mean 4x length. What kind of enlargement only elongates? Distance enlargements only elongate. By logic, that implies a long, narrow increase in size. A circle will become a very long oval; a square will become a long rectangle.

The one image I was not able make (not a PS user) is a single tile stretched to four times its length, but retain its width. Using your definition of magnification, that wild represent 4x, but not 4x life-size.