This puzzling business of "35mm lens equivalent"

[Ray]

But perspective, properly defined, does not depend on added content nor upon a feeling of depth.  The ultimate proof of this is a crop of a wide angle shot to show only the area captured by the longer lens will have precisely the same perspective (distortion) measured by any parameters you care to apply.

Really! You reckon the ultimate proof is to effectively convert the wide angle lens to the same focal length as the longer lens in order to prove that differences in focal length have no bearing on perspective? That doesn't sound like a proof relating to perspective, to me. It sounds more like a proof demonstrating that cropping an image produces an identical effect to using a longer focal length.

The sort of proof that would convince me is if someone were to take a few dozen portraits of a number of people from really close up, using a very wide angle lens (say 12mm in 35mm format terms from a distance of 8"), then present to some viewers a number of prints of cropped noses without face, and uncropped noses which include the entire face as background.

To make the experiment as soundly scientific as possible, one would take portraits of a variety of people with different size noses, big honkers, small pudgy noses, thin aquiline noses, and average noses etc. Also, one should not present prints of the same cropped nose that also features in another print with the full face, in order to be as objective as possible. One should also mix in a few cropped noses from images taken with longer lenses from a greater distance. For example, the guy with the big honker might be shot with a 50mm lens from a distance of a couple of feet.

One would then ask the viewers participating in the experiment to identify the images that show the greatest perspective distortion.

My guess would be that all viewers would correctly identify the uncropped images with full face as showing significant perspective distortion, but fail in correctly identifying the cropped noses as showing perspective distortion. What do you reckon?

[Jim Pascoe]

I have to say that I am behind Mouse on this one.  Wider angle lenses only tend to distort perspective because you have to move in closer to a subject to fill the frame.  The perspective is entirely dependant on the relative position of the lens to the subject.  I can shoot exactly the same head and shoulder shot with my 35mm lens as I can with an 85mm lens from say 8 foot range.  The perspective will be exactly the same regarding noses etc.  It is just with the 35mm lens I will need to crop out a lot of the image, which is a waste of pixels/resolution etc.
With a 24mm lens and a theoretical unlimited resolution I believe I could shoot almost any scene including sports, wildlife etc.  All that would be needed would be to crop the pictures heavily in some cases.  This is of course not practical, but I think the theory is correct.  Depth of field of course is another matter.

On the subject of terminology, I think that an angle of view number would be much more useful than 35mm equivalents.  Whilst I have no problem as things are, as has been pointed out fewer and fewer people have the old reference points of 35mm photography ingrained into their heads.  Anyone brought up with three prime lenses on a 35mm camera has very fixed reference points regarding focal length, but with zoom lenses and the plethora of formats around I think confusion is becoming the norm for newer photographers.  Perhaps I just empathise with people who are easily confused! 

Jim

[Fips]

To turn a wide angle lens into a telephoto lens through cropping in order to claim that focal length has no bearing on perspective sounds like chicanery to me. A big nose in relation to a small face looks different to that same nose cropped, in relation to nothing but a plain background.

But here you neglect the fact that the big nose only comes from being very (or too) close the the subject. If you take a picture with a wide angle from further away, as you would do with a telephoto lens, and then crop it, it will look exactly the same. Mouse is absolutely correct.

EDIT: Sorry, Jim was typing faster.

[hjulenissen]

I would gladly and immediately adopt a better one if someone comes with it.

For compact cameras and lenses that will only be used on a given sensor-size:
"this camera/lense will cover 15 degrees of your scene horizontally"

I think that is more intuitive to the novice camera users.

Unfortunately, when the same lense may be used on "FF" and "crop" sensors, this explanation has less value.

-h

[Ray]

But here you neglect the fact that the big nose only comes from being very (or too) close the the subject. If you take a picture with a wide angle from further away, as you would do with a telephoto lens, and then crop it, it will look exactly the same. Mouse is absolutely correct.

EDIT: Sorry, Jim was typing faster.

I do indeed neglect that fact, because I don't regard it as a fact. I can make the nose as big or as small as I want whatever the lens I've used from whatever distance, simply by interpolating or downsampling the cropped image of the nose and making either a big print or a small print.

The size of the nose itself, separate from its background, is not the issue regarding perspective. That's the point I'm trying to get across. It's the size of the nose in relation to its background of other facial features and in relation to other more distant features behind the person, that contribute to a sense of distorted perspective.

If one crops away all the background stuff that is necessary to provide the sense of distorted perspective that a wide-angle lens can produce from close up, then you have not only effectively converted the wide-angle lens to a longer focal length, but have also lost much (if not all) of that sense of distorted perspective.

This all seems very clear to me. I can't understand your difficulty. Cropping any image reduces the angle of view and effectively converts the lens used to a longer focal length. There's no dispute about that whatsoever. However, if you were given an assignment to produce amusing photos of people with distorted perspective and big noses, I suspect you would choose a wide-angle lens. I'd be very susrprised if you were to take this so-called authoritative advice that perspective has nothing to do with choice of focal length and pick any lens at random.

[EduPerez]

[...]However, if you were given an assignment to produce amusing photos of people with distorted perspective and big noses, I suspect you would choose a wide-angle lens.[...]

No: I would choose to get very close to the subject; and to get all the face inside the frame, I would probably need a wider lens, or a larger sensor, or several shots merged together, ... . The distorted perspective that you mention does not come from the focal length, it comes from the distance; the focal length only serves to get back the angle of view that you lost by moving the camera.

[theguywitha645d]

If distance is the sole criteria for perspective then why do the lines in my example converge at different rates--this is a pretty fundamental concept in linear perspective where changing the rate of convergence is changing perspective. And you can look at each image and see the apparent depth of each image is different. Seeing is believing.

The problem with using the ratio of image size/object distance is which two object define perspective. And my example show that perspective is changing, yet the image size ratio is held constant.

The crop comparison is a false argument simply because you are no longer comparing the uncropped to cropped image. You are comparing two identical images which naturally would look the same. You need to compare the cropped to the uncropped because the the change in relative scale is important.

(The other problem is, perspective in photography is not simply defined be the ratio of image size. I did git a source and you will note that the entry covers 7-8 pages.)

[theguywitha645d]

BTW, the image size and distance is a ratio, not just a single distance. If the ratio of images sizes is 2:1, to keep that ratio I can actually do that in an unlimited number of object distances as long as I maintain a 2:1 ratio of object distances.

[EduPerez]

If distance is the sole criteria for perspective then why do the lines in my example converge at different rates--this is a pretty fundamental concept in linear perspective where changing the rate of convergence is changing perspective. And you can look at each image and see the apparent depth of each image is different. Seeing is believing.
[...]

But the lines in your example do not converge at different rates (because they are the same lines). Do not believe me? Open both images on separate layers, and make the top one semi-transparent; if you move it properly, you can see how the lines match.

[theguywitha645d]

But the lines in your example do not converge at different rates (because they are the same lines). Do not believe me? Open both images on separate layers, and make the top one semi-transparent; if you move it properly, you can see how the lines match.

You are not following the conversation. The difference in magnification does matter--you don't print your cropped images proportionally smaller than your uncropped images; no, you want an 8x10 or 16x20. By your definition, I can take any image, taken at any distance, with any lens and rescale it to fit any radial lines you would like--linear perspective is radial, but it is the relative rate of convergence that determines our perception of depth, not an absolute one.

At the scale they are presented in my example, the lines are converging at different rates. You can even see the angles are different. Perspective has changed and a viewer will perceive those differences.

Perspective is the apparent depth in a 2-D image; how a viewer perceives depth. It is not an absolute measure in an absolute frame.

[EduPerez]

[...]By your definition, I can take any image, taken at any distance, with any lens and rescale it to fit any radial lines you would like[...]

No, you can't: unless you distort the image by changing the aspect ratio, the angles are not going to change, no matter how you crop or rescale the image.

[...]You can even see the angles are different.[...]

No, they aren't; just try it, measure them: 29 degrees, give or take, on both images.

[Eric Myrvaagnes]

I am appalled that there is such widespread misunderstanding among photographers about this. Any of you that understand simple geometry will realize that Mouse is absolutely correct.

Conversely, those of you who dispute Mouse do not understand geometry (or the nature of "perspective").

Eric

[theguywitha645d]

No, you can't: unless you distort the image by changing the aspect ratio, the angles are not going to change, no matter how you crop or rescale the image.

Sure I can. Your have never worked with radial lines and linear perspective.

No, they aren't; just try it, measure them: 29 degrees, give or take, on both images.

But there are two line, how can you get one number?

Left image:

Top line: 11.9 degrees
Bottom line: -17.6 degrees

Right image:

Top line: 11.5 degrees
Bottom line: -16.9 degrees

Measured in Photoshop extended CS5.5. Measured twice to smooth errors. And yes, the difference is great enough to be perceived.

[Jim Pascoe]

I am appalled that there is such widespread misunderstanding among photographers about this. Any of you that understand simple geometry will realize that Mouse is absolutely correct.

Conversely, those of you who dispute Mouse do not understand geometry (or the nature of "perspective").

Eric

Agreed.  I think part of the problem is that a few people here are arguing different points without realising it.

Jim

[theguywitha645d]

I am appalled that there is such widespread misunderstanding among photographers about this. Any of you that understand simple geometry will realize that Mouse is absolutely correct.

Conversely, those of you who dispute Mouse do not understand geometry (or the nature of "perspective").

Eric

Expressing indignation is not an argument. And the fact you dismiss the example image shows you don't understand geometry, let alone perspective.

[theguywitha645d]

Agreed.  I think part of the problem is that a few people here are arguing different points without realising it.

Jim

Jim, it goes deeper than that. Many people don't know what they are arguing, but just trying to affirm a tidbit of "knowledge" they picked up somewhere.

[EduPerez]

But there are two line, how can you get one number?

I always get one number when I measure angles... I do not use PS, but you are probably measuring the angle of each line with respect to an (imaginary) horizontal line; just make a subtraction and you should get the same number as me.

Left image:

Top line: 11.9 degrees
Bottom line: -17.6 degrees

Right image:

Top line: 11.5 degrees
Bottom line: -16.9 degrees

Measured in Photoshop extended CS5.5. Measured twice to smooth errors. And yes, the difference is great enough to be perceived.

Please, repeat your test: grab the full-res version of the image, draw the lines on it, and measure the angle; now crop and enlarge at will (be very sure to preserve the aspect ratio), and measure the same lines again.

[Slobodan Blagojevic]

This discussion reminds me of an old joke: a guy enters a highway in the opposite direction. Police spotted him and broadcasts a warning: "Attention all drivers... There is one idiot driving in the opposite direction." The guy heard the warning as well and says to himself: "Ha! Just one!? Look how many there are!"

[EduPerez]

But then you know I can take any image regardless of objective distance, focal length, etc. and match them to one set radial lines by simple scaling...

But you have already proven the opposite, haven't you? You took an image, scaled it at your will, and obtained the same set of lines; how do you plan to obtain a different set of lines now?

Let's suppose your lines measured 30 degrees on the original; you cropped and scaled the image yourself, and the resulting lines where also 30 degrees apart. Could you make them measure 15 or 45 degrees? Without changing the aspect ratio?

[Ray]

No: I would choose to get very close to the subject; and to get all the face inside the frame, I would probably need a wider lens,

You are not sure?? You think you might need a wide-angle lens, but stitching images with a moderate telephoto lens with a macro facility might be a sensible alternative?

The distorted perspective that you mention does not come from the focal length, it comes from the distance;

It comes from the distance to what, precisely? The distance to the nose? The distance to the eyes? The distance to the ears? The distance to some background object outside the FoV of a longer focal length lens?

the focal length only serves to get back the angle of view that you lost by moving the camera

Who's moving the camera? I thought we were talking about perspective from the same shooting position using different focal lengths of lenses. If you crop the wide-angle shot to the same FoV as the telephoto shot, you've effectively increased the focal length of that wide-angle lens. If you stitch images to increase the FoV, you've effectively reduced the focal length of the system and created a wide-angle lens equivalent, or at least a wider-angle lens equivalent.

If your point is that the actual and nominated focal length marked on the lens has in itself no fixed and unchangeable bearing on the perspective of a processed image, from a given shooting position, if one can use various strategies to either effectively increase or reduce focal length, such as applying cropping or stitching a number of images together, then I agree completely.

It's the effective focal length that always counts, not the nominated FL marking on the lens. That's understood surely. The effective focal length of the lens depends not only on the nominated focal length of the lens but the size of the sensor and the final FoV of the processed image.

In summary, the sense of perspective in any image is largely dependent upon two factors; the shooting position and the effective focal length of the lens, often described in 35mm format terms.