You poo-pood my comment

The first one was taken with the zoom lens set to 100mm and 60" away. The second one was taken with the zoom lens set to 50mm and 30" away.
I think this proves what I said that if you move closer to an object, the image is the same if you use the correct lens.
The object in the photos is the "Rover" badge and to my eyes they are the same.
Computer geeks can find out what lens setting each photo was taken with.

I'm not sure what you are trying to prove, but if it's about perspective then you need a 3D subject rather than a flat one.

I can see that the images are not the same though, as they show a different field of view and a slightly different magnification.

If you check the exifs of those images you'll find they're closer in focal length to each other than what you state.

Image 1:
Focal Length: 95.0mm (35mm equivalent: 142mm)
Aperture: ƒ/5.6

Image 2
Focal Length: 58.0mm (35mm equivalent: 87mm)
Aperture: ƒ/4.5

Not withstanding that, as John said, the subject shown is practically flat. If you photograph a newspaper page at different focal lengths you wouldn't expect the resulting photos of that page to look any different to each other apart from lens distortion differences.

Try the experiment again with the badge around a metre in front of a discernible background (say a newspaper page) and there will be quite noticeable differences.

Then try it again at the extremes of your telephoto, 18mm and 270mm and see what happens.

You said:
"I think this proves what I said that if you move closer to an object, the image is the same if you use the correct lens. "

What you really mean is
"I think this proves what I said that if you move closer to an object, the object appears the same if you use the correct lens. "

The "image" will not be the same as all other elements in front or behind of the object your photographing will change in appearance with differing focal lengths, and as pointed out by John your subject in this case is pretty much 2 dimensional.

Test your theory with your stated lenses.
Try shooting something with a bit of depth to it.
As said above shooting something that's flat is pointless

https://flic.kr/p/JxFiYZ

https://flic.kr/p/K3QYad

I had thought this topic was sorted. Ah well.

To prove that isn't the case, imagine being somewhere in the Scottish Highlands with a gorgeous sunset you wish to capture featuring Ben Nevis as you just happen to be staying close by.
However you find yourself in a location where Ben Nevis is completely obscuring most of the sky, let alone the sun. You take a photo anyhow and then decide to drive somewhere a bit further away so you can see both Ben Nevis and the setting sun. You now get your photograph as Ben Nevis is no longer that close to obscures the sun. But how though could those two images ever be the same no matter what lens you used? In this instance you've moved further away not closer but I'm sure you wouldn't argue that is the reason for the difference?

I was out with the family on Saturday in hilly terrain, lots of long views but plenty of distracting tree lines and tangly forest textures in behind. I found that by standing back from my portrait subjects and zooming in to 105mm, my backgrounds became less distracting because there was less to see in behind the subject ..... the perspective difference had reduced the field of view in behind, so there was a more uniform range of textures and colours, plus the background was more OOF, making the subjects stand out nicely in front.

I quickly made this diagram to demonstrate the principle as I understand it. At the top is a telephoto shot and at the bottom is a wide angle shot.




In both resultant images the subject would be the same size (it occupies the same proportion of the image, ie. the distance between the black lines which indicate the image edges). However, you can see that the background will be very different indeed (red arrows). Furthermore, on the issue of perspective distortion and the need for a 3D subject in order to demonstrate it, notice the distance from the photo edge (the black lines) of the front of the subject and the back of the subject. In the telephoto shot (top) it is very similar while in the wide angle shot the difference is much greater, and this is what produces perspective distortion (big noses in portraits being the most common example given).

So, while the subject overall may occupy the same space in the photo (note that I don't say it's the same size), the images will be very different.

As many of the examples so far mention backgrounds, I've just done these two examples to concentrate on the subject. Both were taken with the DA 20-40, using the on-board flash, and in both the camera was level with the headlamps of the model car. The second (at F=40mm) was taken from twice the distance compared with the first. Each image has been cropped to consider only the differences in the perspective of the subject itself:







Cheers.
Philip

Reminds me of this:

Be careful stealing images off fashion photographers can land you with a big bill

http://www.stepheneastwood.com/

--

http://stepheneastwood.com/tutorials/Tutorials_Lens_Perspective.htm

Certainly not passing this off as my own, in case anyone actually thought that.

I'm not stealing anything. Just googled "portrait focal length" and went to the image tab.
Grabbed one near the top that was on pintrist to show here.

That's an excellent example of the flattening effect that telephotos have Richard, if you looked at the first and last images side by side you'd be forgiven for thinking they were sisters rather than the same girl.

Yes, and look at what's happened to the background as well. .....

Thanks for all the comments. The badge is a Rover badge taht was fitted to 200 and 400 models, it is definately not 2D, it is 3D, I should know, I CAD modelled it.

MrB also proves my point, you cannot break the laws of physics!

JAK, no insult intended, but I think a trip to Specsavers is needed.