# Why isn't the size of an object in macro image exactly proportional to the ratio of the focal length and distance in front of that?

Using a Canon 550D with a EF 100mm f/2.8 Macro USM lens, I can make a 1:1 macro photo at shortest film plane to subject distance of 310 mm, thus getting 22 mm of a scale on the APS-C sensor, which is 22.5 mm wide. Photo is here:

The focal length of this lens is 100 mm, so with a film plane to subject distance of 310 mm, I expect 210 mm from object to "cross" point, and another 100 mm (given by lens) from "cross" point CCD, as shown on this drawing:

(2015-01-25: Note that drawing was updated to fix wrong terms)

But with the ratio of 2.1 to 1 between distance from object to "cross" point and from "cross" point to CCD (210 mm to 100 mm), I would expect the scale to be 2.1 times smaller on the CCD, which is clearly not the case, since 22 mm of scale can show on the 22.5 mm wide APS-C sensor.

Where is the mistake in my calculation above ?

The focal length of a lens only applies to objects at infinity, and is the distance (𝑓 in the diagram below) between the lens and the sensor when such an object is in focus. The focal point (F) would actually be ON the sensor.

As an object gets closer to the sensor, the focal point moves away from the lens, meaning the lens has to be moved away from the sensor to keep the object in focus. This is why many lenses lenses get longer as you focus on closer objects.

The distance from the sensor to the object in focus is called the focal distance, and is indicated by the scale on your lens.

The 1:1 ratio on your macro lens represents the size of the image on the sensor relative to the object's actual size, and since you have demonstrated you can see 22mm of the scale on the 22.5mm sensor, this is what should be expected (as 22:22.5 is more or less exactly 1:1).

It should be noted here that due to their construction, many lenses have a physical length which is longer or shorter than their focal length. Telephoto lenses are defined as lenses whose length is shorter than the focal length, using a combination of lens elements that mimic the effects of a single lens as in the diagram above. And extreme wide-angle lenses can have focal lengths of 20mm or less but where the rear element of the lens is more than 20mm from the sensor of the camera.

• So his labeled focal point is really what, the node? – JDługosz Jan 24 '15 at 23:41
• Well it doesn't really represent anything, as the light rays don't travel in straight lines from the object to the sensor like that; they are diverted by the lens. – NickM Jan 24 '15 at 23:58
• It just bothers me that such a nice drawing is incorrect; worried someone will remember that only, out of context. Hmm, that works for a pinhole, so the labeled point is an approximation to a lens position. – JDługosz Jan 25 '15 at 5:54
• Yes, it's true for pinhole cameras, but misleading when considering lenses. I mocked up some diagrams to show how the lenses with different focal lengths can achieve this at nickminers.com/macro.png – NickM Jan 25 '15 at 11:09
• @EquipDev the best way to ask these questions would be to post another question on the site proper, rather than in a comment; that way everyone who visits can see them and answer them. Many questions already answered might help you out, so try searching the site to see whether this is the case before posting new questions. Good luck! (here are some which might help) photo.stackexchange.com/questions/25559/… photo.stackexchange.com/questions/38192/… – NickM Jan 25 '15 at 19:38