BetterPhoto Q&A
Category: Problems with Photo Equipment - Tips & Tricks

How to confirm zoom lens specifications

There is some scuttlebut on the internet (shocking!) that the actual deliverd zoom ratios marked on our digital cameras are NOT being delivered, and are just so much marketing hooey.

So, I'm stuck trying to check the real zoom ratio of a lens regardless of what the manufacturer says. Can anyone help me?

I tried this SIMPLE test: If I shoot two pictures of a yard stick on the floor from my tripod mounted camera, with the yard stick exactly going through two opposite corners of the image, one picture taken with the wide angle end of the lens, and the other picture taken with the telephoto end of the lens, camera body distance to the yard stick exactly the same for both images, then measure and compare the lengths of the captured part of the yardstick in each picture, how do I then assess the resulting numbers and figure out a REAL focal length zoom ratio?

Specifically on the Konica Minolta DiMage 7, 7u, 7i, 7hi, A1m, A2 and A200 digital camera:

Focal lengths: 7.2-50.8mm (marked)
35mm equivalent= ~28-200mm (marked)

Marked: "7x zoom"

50.8/7.2 = ~7.056x zoom
(7.2/50.8 = ~0.14 if it matters)

200/28 = ~7.14x zoom
((28/200 = ~0.14 if that matters)

Now the test pcitures of a yard stick:

7.2mm (~28mm) wide angle captures ~22.21875 units from the yard stick

50.8mm (~200mm) telephoto captures ~6.04375 units from the yard stick

22.2/6.04 = 3.67x - HUH?!?
(6.04/22.2 = 0.27 if that matters)

...so, what's the relative REAL x zoom ratio? 3.67x? Not 7x?!?

How do I check this? Where have I gone wrong (or right!)?

Let me try another lens and camera. I then loaded my Tamron 28-200mm xoom onto my Minolta 507si/600si/650si camera and did the same exploration:

28-300mm (marked)

300/28 = 10.7x zoom
(28/300 = 0.093 if that matters)

Now the test pcitures of the yardstick:

28mm wide angle captures ~50 units from the yard stick(s)

300mm telephoto captures ~8 units from the yard stick

50/8 = 6.25x - HUH?!?
(8/50 = 0.16 if that matters)

...so, what's the relative REAL x zoom ratio? 6.25x? Not 10x?!?

ALL other references over the internet want me to measure the distance from the image (film plane or sensor plane) to the "simple" lens, plus the distance from the simple lens to the subject, which I guess is the total distance from the subject to the film/sensor plane. I can do that, but why? It was the same for each picture.

Is there ANY way to calculate relative focal length ("relative" is all I'm after) between two different iamges where the same item is captured at different sizes because of focal length zoom - in the first case, a 3.67x iamge size ratio, and in the second case, a 6.25x image size ratio. So what, then, are the focal length ratios?

Am I w-a-y off because I'm shooting close (~2-3 feet away), and instead if I measured the zoom ratios at infinity focus, that would make all the difference? I don't have a yard stick that long! ;-)

Thanks to all who even read this far, let alone may have some insight or reference on where to look next to check ACTUAL zoom ratio.

Stuck in mathematics hell,

Peter Blaise
peterblaise@yahoo.com
http://www.peterblaisephotography.com/

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July 12, 2005

Please excuse the typos - the Tamron is the 28-300 model zoom, not the "28-200 xoom".

The meaning of "units from the yard stick" probably would have been less ambiguous if I had written "units OF the yard stick" as I did NOT change the camera distance FROM the yard stick between shots, rather, I captured units OF the yard stick in an image.

Clearer now?

Thanks for bearing with me. ;-)

Peter Blaise

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July 12, 2005

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July 12, 2005

Peter,
I think the confusion comes from trying to interchange "zoom ratio" with "magnification ratio". Maybe marketing has intentionally muddied the lines between the two.

"Zoom ratio" is the ratio between the longest and shortest focal lengths of the lens. Your first calculation of 50.8/7.2=7 shows that the advertised 7x zoom is correct.

Your test with the yardstick was demonstrating the "magnification ratio" of the zoom lens. You proved that zoom ratio and magnification ratio are not the same. Basically, if your zoom ratio is 7x, it doesn't mean that an object in your viewfinder will appear 7 times it's size when you zoom in on it.

Focal length and magnification are not a direct ratio.

Does this help?

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July 12, 2005

Digital (2/3 size) = short tele
35MM = normal
6x4.5 = moderate wide angle

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July 12, 2005

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July 12, 2005

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July 13, 2005

Thanks, Chris V.,

I guess what you are saying is that either:

(a) you do not know a translation formula to convert from:

- the known ratio of the measured size differences between the same object shown larger and
smaller in 2 different pictures, and

- converting into the focal length ratio of the 2 different lenses used to take those pictures,

or, you are saying:

(b) there is no correlation between:

- the ratio of the smaller and larger sizes of an object in the 2 pictures, to

- the ratio of the shorter and longer focal lengths of the 2 lenses that took those pictures.

Which?!?

I am not expecting the ratios to be equivalent.

I know that focal lengths, angle of view, magnification, and object sizes change at different
rates (ratios) from each other.

For instance, focal length and angle of view are inversely related and non-linear, in other words:

- a large focal length number matches a small angle of view number; and

- a small focal length number matches a large angle of view number.

However (not that it matters) magnification and focal length are "versely" related (the opposite
of "INversely"?), such that:

- a large focal length number matches a large magnification number; and

- a small focal length number matches a small magnification number,

... and so on. Anyway ...

I want to convert from one ratio to another.

I want to convert from:

- a measured size of 2 different images of a subject

converting into:

- the ratio of the 2 focal lengths that took those 2 pictures.

In my 2 pictures, everything BUT the focal length stays EXACTLY THE SAME.

In changing the focal lengths (or magnification), the resulting image size also changes - what's
the relationship?

So, if all I can measure are the 2 subject image sizes (and derive the ratio between them), then,
how do I derive the focal length ratio between the two pictures?

The object stays the same.

The distance to the object stays the same.

The form factor of the film/sensor stays the same.

Only the focal length (magnification) changes.

As a result, the size of the object in each image changes.

All I can do is measure the object sizes.

(I suppose I could measure the distance from the camera to the object.)

I know that angle of view changes at a different rate than focal length as you zoom. So, the
ratio of the 2 angles of view between the 2 pictures does not equal the ratio between the 2 focal
lengths used.

Same for the item in the picture - the ratio of the 2 sizes does not equal the ratio of the 2 focal
lengths of the lenses that took the 2 pictures.

I think I will need to study other examples that I can prove a relation, then return to the problem
at hand. I could play with the isosceles triangles in the pictures and find a formula that divines the
ratio of those 2 angles the ruler, and then find an equivalent curve on a known chart, and see
where my test falls.

In other words (WORDS!!!) I need to draw PICTURES, or I'll be as lost as are poor Kerry W, and
Samual S.!!!

Click!

Love and hugs,

Peter Blaise Monahon
peterblaise@yahoo.com = peterblaise @ yahoo . com
http://www.peterblaisephotography.com/

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July 13, 2005

	The geometry in question! Can you deriving focal length ratio from measured object size ratio in 2 images? Peter Blaise Monahon

Thanks, Chris V.,

I guess what you are saying is that either:

(a) you do not know a translation formula to convert from:

- the known ratio of the measured size differences between the same object shown larger and
smaller in 2 different pictures, and

- converting into the focal length ratio of the 2 different lenses used to take those pictures,

or, you are saying:

(b) there is no correlation between:

- the ratio of the smaller and larger sizes of an object in the 2 pictures, to

- the ratio of the shorter and longer focal lengths of the 2 lenses that took those pictures.

Which?!?

I am not expecting the ratios to be equivalent.

I know that focal lengths, angle of view, magnification, and object sizes change at different
rates (ratios) from each other.

For instance, focal length and angle of view are inversely related and non-linear, in other words:

- a large focal length number matches a small angle of view number; and

- a small focal length number matches a large angle of view number.

However (not that it matters) magnification and focal length are "versely" related (the opposite
of "INversely"?), such that:

- a large focal length number matches a large magnification number; and

- a small focal length number matches a small magnification number,

... and so on. Anyway ...

I want to convert from one ratio to another.

I want to convert from:

- a measured size of 2 different images of a subject

converting into:

- the ratio of the 2 focal lengths that took those 2 pictures.

In my 2 pictures, everything BUT the focal length stays EXACTLY THE SAME.

In changing the focal lengths (or magnification), the resulting image size also changes - what's
the relationship?

So, if all I can measure are the 2 subject image sizes (and derive the ratio between them), then,
how do I derive the focal length ratio between the two pictures?

The object stays the same.

The distance to the object stays the same.

The form factor of the film/sensor stays the same.

Only the focal length (magnification) changes.

As a result, the size of the object in each image changes.

All I can do is measure the object sizes.

(I suppose I could measure the distance from the camera to the object.)

I know that angle of view changes at a different rate than focal length as you zoom. So, the
ratio of the 2 angles of view between the 2 pictures does not equal the ratio between the 2 focal
lengths used.

Same for the item in the picture - the ratio of the 2 sizes does not equal the ratio of the 2 focal
lengths of the lenses that took the 2 pictures.

I think I will need to study other examples that I can prove a relation, then return to the problem
at hand. I could play with the isosceles triangles in the pictures and find a formula that divines the
ratio of those 2 angles the ruler, and then find an equivalent curve on a known chart, and see
where my test falls.

In other words (WORDS!!!) I need to draw PICTURES, or I'll be as lost as are poor Kerry W, and
Samual S.!!!

Click!

Love and hugs,

Peter Blaise Monahon
peterblaise@yahoo.com = peterblaise @ yahoo . com
http://www.peterblaisephotography.com/

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July 13, 2005