Is there a linear correlation between focal length and enlargement size?

I was just curious to know whether there was a linear correlation between focal length and magnification. That is to say, if I look through a lens at a square at focal length of 24mm and it is a 100 pixels wide, if I look at the same square at a focal length of 240mm, would the square take up 1000 pixels?

Of course not!
Focal length defines only the angle of view and nothing else.
Enlargement is something that you do (or don’t do) later, in post-processing.
On the sensor, they occupy exactly the same number of pixels.

Take a look here to compare different focal lengths and their corresponding angles of view.

http://www.tamroneurop​e.com/flc.htm

Somehow I know that the answer was no, but I had to ask.

It never hurts to ask, no problems with that!

I like this Tamron site..
It gives really nice visual presentation of focal lengths, angles of view and crop factor.

Great site! I'm going to del.icio.us that one. Certainly helps with my lens buying decisions.

Ephemeral wrote in post #4276026
I was just curious to know whether there was a linear correlation between focal length and magnification. That is to say, if I look through a lens at a square at focal length of 24mm and it is a 100 pixels wide, if I look at the same square at a focal length of 240mm, would the square take up 1000 pixels?

If you double the focal length of the lens on your camera, the linear dimensions of the image of a given subject (left-to-right or top-to-bottom) taken from the same position will double. If you compare the sizes of the image of a given subject (again, taken from the same position) taken with a 24mm lens and a 240mm lens, you will see a 10:1 difference in the linear dimensions of the image.

The dimensions I am referring to are at the film/sensor plane. If you enlarge each image equally (for example, make 4x6 inch prints from both images), you will see the same ratio of image sizes for the portion of the subject you are comparing.

Ephemeral wrote in post #4276026
I was just curious to know whether there was a linear correlation between focal length and magnification. That is to say, if I look through a lens at a square at focal length of 24mm and it is a 100 pixels wide, if I look at the same square at a focal length of 240mm, would the square take up 1000 pixels?

Contrary to what some other folks have told you, the answer is "yes". Well, a qualified yes. (I assume that you're talking about shooting from the same distance.) There are some factors that tend to muddle the numbers a bit, so maybe you'd end up with 950 or 1050 pixels, but in round numbers the focal length is directly proportional to the magnification.

Also, if your square is 100 pixels when shot from 1000 feet with a 240mm lens, then it'll be about 1000 pixels when shot from 100 feet with that same lens.

It sounds like the OP might be talking about cropping that square since it takes up fewer pixels you'd be able to enlarge the square less than if the square filled more of your image.

Nope. Nothing to do with cropping.

If I didn't say pixels but said the width of the projected image of the square on the sensor, then is the answer yes?

This question came about because I was chatting to a friend about the 24-70 vs 24-105 and trying to work out how much more you'd get from the extra reach. I wasn't sure if the focal length was linearly correlated to the projected image size.

My thinking was, and I could be very wrong, if there was a correlation, then the difference you get in magnification of the projected image between 24mm to 59mm would be the same as from 70mm to 105mm. Then you'd get a good idea about the extra reach gained.

Mmmm...I should stick to just pressing the shutter button. It's much simpler.

Hermeto is wrong. SkipD and Doug are right. The effect isn't quite linear - and is most non-linear for wide angles - but it's a reasonable approximation.

So, for example, a 400m lens will make an image on the sensor which is twice as large in each dimension (and therefore occupies four times as many pixels) as that produced by a 200mm lens.

However, the example you gave in your last post is incorrect. From 24mm to 59mm is a factor of 2.5, whereas from 70mm to 105mm is a factor of 1.5. The fact that 59-24 = 105-70 = 35 is irrelevant.

Oh. I see. It's not the actual focal length, it's the ratio between focal lengths.

Ephemeral wrote in post #4282610
Oh. I see. It's not the actual focal length, it's the ratio between focal lengths.

Precisely. Double the focal length and the linear dimension of the image doubles at the film/sensor plane.

As Stewart said, there may be some perceived differences when looking at the performance of the very wide-angle lenses. However, things in the middle of the wide-angle image will be doubled in width or height by doubling the focal length.

Assuming the same aspect ratio, the angle of view of a given focal length will vary linearly with enlargement factor. The pixel count is a different story, because you can choose whether to hold pixel density (ppi) constant or not. If you hold ppi constant, then the number of pixels will change linearly with enlargement. If you keep the number of pixels the same, then the ppi wil change (inversely!) linearly with enlargement.

DrPablo wrote in post #4283023
Assuming the same aspect ratio, the angle of view of a given focal length will vary linearly with enlargement factor. The pixel count is a different story, because you can choose whether to hold pixel density (ppi) constant or not. If you hold ppi constant, then the number of pixels will change linearly with enlargement. If you keep the number of pixels the same, then the ppi wil change (inversely!) linearly with enlargement.

I do not think that Ephermal is even thinking about the printing process ("enlargement"). I believe he was originally referring to the number of pixels (actually, sensor elements) in one direction that the image of a subject would cover on the sensor in the camera.

SkipD wrote in post #4283113
I do not think that Ephermal is even thinking about the printing process ("enlargement"). I believe he was originally referring to the number of pixels (actually, sensor elements) in one direction that the image of a subject would cover on the sensor in the camera.

I guess, I misunderstood the question then..