Why this issue about magnification ratios?

[Mike Buckley]

When a subject is twice the size of the camera's sensor, the magnification ratio is traditionally expressed as 1:2. In that situation the number on the left represents the relative size of the sensor and the number on the right represents the relative size of the subject. Yet when the subject is half the size of the camera's sensor, the magnification ratio is traditionally expressed as 2:1. In that situation the meaning of the numbers is reversed with the number on the left representing the relative size of the subject and the number on the right representing the relative size of the sensor.

What is the rationale of reversed expressions of magnification ratios depending on the situation? How did that reversal come to be?

I ask because it seems more logical and intuitive to me that the meaning of the numbers on the left and right sides should always be constant. As an example, the number on the left could always represent the relative size of the sensor and the number on the right could always represent the relative size of the subject. In that situation, when the subject is half the size of the sensor the magnification ratio would be 1:0.5 (rather than 2:1 as traditionally expressed).

[marlunn]

Ah well you cursed that one as soon as you stated 'it seems more logical'
While one would hope that 'logic' has a home in technology it is often proven to be a false hope and 'tradition' or 'cos, thats why' rules - sorry, no answer to your conundrum and probably added nothing to the discussion but wasted screen space

[george013]

When a subject is twice the size of the camera's sensor, the magnification ratio is traditionally expressed as 1:2. In that situation the number on the left represents the relative size of the sensor and the number on the right represents the relative size of the subject. Yet when the subject is half the size of the camera's sensor, the magnification ratio is traditionally expressed as 2:1. In that situation the meaning of the numbers is reversed with the number on the left representing the relative size of the subject and the number on the right representing the relative size of the sensor.

What is the rationale of reversed expressions of magnification ratios depending on the situation? How did that reversal come to be?

I ask because it seems more logical and intuitive to me that the meaning of the numbers on the left and right sides should always be constant. As an example, the number on the left could always represent the relative size of the sensor and the number on the right could always represent the relative size of the subject. In that situation, when the subject is half the size of the sensor the magnification ratio would be 1:0.5 (rather than 2:1 as traditionally expressed).

Read 1:2 as 1/2=0.5. Image size : object size. Sensor size is not involved.
A wine bottle of 20cm high that produces an image of 15mm on the sensor will make a magnification of 15/200=0.075. Just to use another figure. If you're not sure anymore, use this example: must be less than 1.
This is another one too. Is it an object or a subject?

George

[Mike Buckley]

Read 1:2 as 1/2=0.5. Image size : object size. Sensor size is not involved.

Sensor size is traditionally referenced, not image size. Even so, if one wants the number on the left to represent the relative image size when it is smaller than the object size, why would it not also be on the left when it is larger than the object size?

[DanK]

George is right: sensor size is not involved. The ratio as commonly expressed is the size of the image as projected onto the sensor to the size of the object. (You have the ratios backwards.). So 5:1, which is the magnification of the MP-E 65, means that the image size is 5 times as large as the object size (for example, see https://luminous-landscape.com/canon-mp-e-65/)

Sensor size only comes into play when you have to determine how large the projected image is relative to the total image captured, that is, framing. I use my canon macro lens on two cameras, one a FF and one a crop. At minimum focusing distance, the size of the projected image is the same with both cameras (it's a function of the lens, not the surface onto which the image is projected). However, the image takes up a much larger share of the total space with my crop sensor. That's one of two reasons why I almost always do bugs with my crop sensor camera. The pixel density is higher, and so I get more pixels on the subject.

[george013]

Sensor size is traditionally referenced, not image size. Even so, if one wants the number on the left to represent the relative image size when it is smaller than the object size, why would it not also be on the left when it is larger than the object size?

It's just optics, gonio. There's nothing as a relative reference. Your wine bottle is 20cm/200mm. The image on your sensor is 15mm. Independent of the sensor size. Since we both know that the image must be smaller the the winebottle itself, you can always tell which one must be on the left.
When you've a FF camera that's able to shoot DX, changing from FF-mode to DX-mode doesn't change the magnification.

George

[Mike Buckley]

The ratio as commonly expressed is the size of the image as projected onto the sensor to the size of the object.

I can't begin to tell you how many times I've seen the ratio explained as the size of the sensor, not the size of the image as projected onto the sensor, though at first glance there seems to be no difference between the two, perhaps especially to those like me are who are not technically inclined. This might be an example of why you can't believe everything you read on the Internet.

[JohnRostron]

When a subject is twice the size of the camera's sensor, the magnification ratio is traditionally expressed as 1:2. In that situation the number on the left represents the relative size of the sensor and the number on the right represents the relative size of the subject. Yet when the subject is half the size of the camera's sensor, the magnification ratio is traditionally expressed as 2:1. In that situation the meaning of the numbers is reversed with the number on the left representing the relative size of the subject and the number on the right representing the relative size of the sensor.

No, the numbers are not reversed. The relative magnitudes are exactly as before. The number on the left (2) is the size of the image relative to the size of the subject (1).

John

[DanK]

No, the numbers are not reversed. The relative magnitudes are exactly as before. The number on the left (2) is the size of the image relative to the size of the subject (1).

John

Right, sorry, I misread it. It's just a matter of convention, of course, but the convention is image sizebject size

[george013]

A ratio of a:b means a divided by b. A ratio of 1:2 is 0.5. A ratio 2:1 is 2.
A magnification bigger as 1 means the image is bigger as the original.
A magnification less as 1 means the image is smaller as the original.
And all in absolute sizes.

I don't think there's much more.

George

[miatab]

The one on the left should be the wine bottle, and it should be half empty, and the one on the right should be the wine glass, and it should be empty. The one in the middle should be me and i'd be half full.

[mikesan]

I can't begin to tell you how many times I've seen the ratio explained as the size of the sensor, not the size of the image as projected onto the sensor, though at first glance there seems to be no difference between the two, perhaps especially to those like me are who are not technically inclined. This might be an example of why you can't believe everything you read on the Internet.

You may well have seen the term "size of the sensor" frequently used in discussions about (magnification) ratio. I would bet that, in each and every case, what was actually meant was "the size of the image (as projected) on the sensor". It is an example of the very careless use of language which is rampant on the internet and elsewhere. This can easily lead to a lack of confidence in what one reads especially where ambiguity leads to misinterpretation.

[Andrew1]

https://en.wikipedia.org/wiki/Macro_photography

http://www.discoverdigitalphotograph...o-photography/

[mikesan]

When a subject is twice the size of the camera's sensor, the magnification ratio is traditionally expressed as 1:2. In that situation the number on the left represents the relative size of the sensor and the number on the right represents the relative size of the subject. Yet when the subject is half the size of the camera's sensor, the magnification ratio is traditionally expressed as 2:1. In that situation the meaning of the numbers is reversed with the number on the left representing the relative size of the subject and the number on the right representing the relative size of the sensor.

What is the rationale of reversed expressions of magnification ratios depending on the situation? How did that reversal come to be?

I ask because it seems more logical and intuitive to me that the meaning of the numbers on the left and right sides should always be constant. As an example, the number on the left could always represent the relative size of the sensor and the number on the right could always represent the relative size of the subject. In that situation, when the subject is half the size of the sensor the magnification ratio would be 1:0.5 (rather than 2:1 as traditionally expressed).

Your logic and intuition are correct. By generally accepted convention, magnification when expressed as a ratio places the relative size of the image (as projected on the sensor) first, followed by the relative size of the object (subject).

When a subject is twice the size of the camera's sensor, the magnification ratio is traditionally expressed as 1:2.

However it should be noted that, again by convention, the ratio is expressed such that the relative size of the object is assigned a value of unity (1). Thus in the first case above the magnification ratio is conventionally expressed as 0.5:1 (which is mathematically equivalent to 1:2). Alternatively the magnification is often expressed, in this case, as 0.5X indicating that the image is one half the size of the object.

Yet when the subject is half the size of the camera's sensor, the magnification ratio is traditionally expressed as 2:1. In that situation the meaning of the numbers is reversed with the number on the left representing the relative size of the subject and the number on the right representing the relative size of the sensor.

There has been no reversal of numbers. The first number (2) represents the size of the image (on the sensor) relative to the size of the object (1). Here again the magnification may be expressed as 2.0X, indicating that the image is twice the size of the object.

[William W]

. . . However it should be noted that, again by convention, the ratio is expressed such that the relative size of the object is assigned a value of unity (1). etc . . .

I concur. Good point to mention, because I think that (lack of sticking to) the convention is a key point to any confusion which is picked up on the www - especially if the commentary is not specific and not clear in its meaning. (As mentioned in Post #12)

I think that most Macro-enthusiasts/experts/technical people use the 'unity' ratio.

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(aside as another example) Similarly, Camera (both Cine and Still) Aspect Ratios, "by convention" were expressed as X:1 (the second numeral being unity).

Nowadays, it is more common to see 3:2 and 4:3 etc for camera/sensor Aspect Ratios, (not 1.5:1 and 1.33:1 etc). And probably for most, in the case of describing Camera/Sensor Aspect Ratios, 3:2 is more easily visually understood than thinking about 1.5:1.

But Cinematography still generally holds to the convention of using X:1 and so we get (perhaps seemingly cumbersome ratios) - such as 2.35:1 or 2.39:1 (common for "Widescreen")

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(aside as an interesting comment) The Mathematics Curriculum in Schools (here) teaches that it is Mathematical Convention and also best practice to express any Ratio using the Simplest Whole Numbers.

WW