Wednesday, October 21, 2009

Apparent Perspective and Focal Length






























Many photographers think focal length affects perspective. They think wide angle lenses exaggerate perspective, and telescopic lenses flatten perspective.

Technically speaking, that's not true. All focal lengths show perspective identically.

Some of you might be thinking, "But I've seen exaggerated perspective with wide angle lenses and flattened perspective with telescopic lenses". So, what's going on?

Here's the way it's actually working:

In order for a wide angle lens and a telephoto lens to exactly fit a subject of the same size (such as a yardstick fitting exactly across the length of the frame), the wide angle lens needs to be closer to the subject than the telephoto lens. If we wanted to exactly fill the frame with a yardstick, using a 24 mm lens on a 35 mm format camera, we'd need to be about 2 feet away. To similarly fill the frame with a yardstick, using a 600 mm lens, we'd need to be a little over 49 feet away.

Now imagine there's a second yardstick, a blue one, two feet behind the first one, which we'll say is yellow. As you photograph the yellow yardstick with the 24 millimeter lens from 2 feet away, the blue yardstick will be 4 feet away – twice the distance from your lens – which means the blue yardstick will look half as large as the yellow one in your picture. By comparison, when photographed with the 600 millimeter lens, the blue yardstick is 51 feet away – about 4% farther away than the yellow yardstick 49 feet away, which means it will look 2% smaller in your picture.

Thus, while all lenses actually show perspective the same way, the way we use lenses, due to their focal lengths, gives us the appearance of different perspectives. The way wide angle lenses usually get used (comparatively closer to subjects) appears to "exaggerate" perspective; the way telephoto lenses usually get used (comparatively farther from subjects) appears to "compress" perspective.

If you used both the 24 mm lens and the 600 mm lens from 49 feet away, and then cropped the 24 mm picture down to where it covered the same area as the 600 mm picture, then compared the two shots side by side, you'd see that the perspective in the two pictures is identical.


View East of Tioga Pass, Near Yosemite National Park, California

All pictures and text are © Mike Spinak, unless otherwise noted. All pictures shown are available for purchase as fine art prints, and are available for licensed stock use. Telephone: (831) 325-6917.

6 comments:

Brian D. Moffet said...

This is the second time I have read this argument, and while technically correct, leaves a bit out of the picture.

In this argument, a basic assumption is made that the distance from the object is the immutable factor. Given that assumption, the angular size of the two objects is the same no matter what lens you use. This is because, by cropping, you are doing exactly the same thing as putting on a longer lens (reducing the angular view of the lens).

However, if you make the other assumption, that the size of the object on the frame (viewfinder) is the immutable factor, then this argument doesn't hold up (as you mentioned).


So my questions are:

1) why is the distance to the lens a more important factor when taking a photograph than the size of the object on the frame? I would think that the size of the object in the frame is more what people are concerned with. I suppose, if you didn't have to worry about grain or pixels, you could crop away to your hearts content and one lens would work fine.

2) what caused the recently flurry of these types of discussions? This seems to be a really popular topic, and I have no idea why. The assumptions to the argument do not seem to provide any insight into making good photographs, (see question 1 above) and I think actually are counter-productive. I am genuinely curious why this is an important issue.

Mike Spinak said...

Brian,

Firstly, I'm not making any assumptions about immutable factors, nor about what is more important. I'm simply making an argument about the physics properties of optics; I'm not making any relative value judgments.

Secondly, regarding "What caused the recent flurry of these types of discussions?" I have no idea what you're talking about. I have seen no recent discussions on the subject.

My reasons for posting this, today, were as follows:

(A) There was a book that I co-wrote, long ago. I was supposed to write a technical chapter about lenses. This got cut from the book, leaving me with some writing material to re-use, at my discretion.

(B) I have a busy day, today, so I thought this would be a good time to recycle some already written material, instead of writing something new.

As for whether it provides useful insight: Either way probably doesn't matter much, but I thought it was an interesting little factoid, for those who like to understand how the world works.

If a situation ever should arise where it matters, then I suspect it is preferable to be working with a more accurate model of reality.

Brian D. Moffet said...

Odd, I have read this argument two times in the last two weeks. Of course I have been going through some of my old magazines and cleaning them out, so for all I know I read it in a year old magazine or something (no, I'm not accusing you of plagiarism or anything, just the timing was interesting.)

As someone who loves optics and physics, it's an interesting factoid. But will it change how people take photos? What do other people think?

G Dan Mitchell said...

Hi.

Not quite buying it... :-)

"Thus, while all lenses actually show perspective the same way, the way we use lenses, due to their focal lengths, gives us different looking perspectives."

What is perspective but a recognition of one way in which objects look relatively different?

And, did you notice that you had to, in the end, state that the examples you used to dismiss the concept of "perspective" "give us different looking perspectives."

It is my perspective that this alone should give you pause. ;-)

Dan

Mike Spinak said...

Hi, Dan,

Let me try putting this a different way.

All focal lengths show perspective identically. A concrete example of this is that all focal lengths show objects twice the distance away at half the size – such as: they all show a 3 foot wide object that is 4 feet away as half the width in the picture frame as a 3 foot wide object 2 feet away.

Many photographers think that wide angle lenses exaggerate perspective, and telescopic lenses compress perspective. In other words, they intuitively believe that wide angle lenses make things smaller, at a quicker rate, as they get farther away; and they intuitively believe that telescopic lenses make things smaller, at a slower rate, as they get farther away. In more concrete terms, they intuitively believe that wide angle lenses show objects twice the distance away at less than half the size; and they intuitively believe that telescopic lenses show objects twice the distance away at more than half the size.

So, for example, if a 24 mm lens showed objects that are twice the distance away at one-quarter the size, then they would truly exaggerate perspective; they would truly be hyper-perspective. In other words, if a 24 mm lens showed a 3 foot wide object at 4 feet away at .25 the width in the frame as a 3 foot wide object 2 feet away, then it would be exaggerating perspective. If a 600 mm lens showed objects that are twice the distance away at three-quarters the size, then they would truly compress perspective; they would truly be hypo-perspective. In other words, if a 600 mm lens showed a 3 foot wide object at 4 feet away at .75 the width in the frame as a 3 foot wide object at 2 feet away, then it would be compressing perspective.

But they don't. All focal lengths show objects that are twice the distance at half the size, not less nor more than half the size regardless of focal length – ergo, they all show perspective identically.

zergworld said...

In Volume 5 of the magazine Petersen's Photographic Digital Photography Guide, the the cover article is "Choosing and Using Lenses"

In that article, the author repeatedly states that a benefit of long lenses is compression. I emailed the editor to express some dissatisfaction with the mis-representation, given that it implies shooting giraffes at the zoo with a superzoom will cause compression as opposed to simply cropping the field of view.

We exchanged a few emails, but the upshot is that he was not persuaded and said we can "agree to disagree". It seems that the myth that focal length affects perspective is wide-spread, well-established, and ingrained, despite the clear evidence to the contrary.

In this case and others, thorough analysis is easily replaced by association recognition that does not by itself determine causal connections without said analysis.

Although we are bound by physical laws, general understanding and communication of these are likely to remain fuzzy, imprecise, and experience/association oriented. However, for those who take the time to commit to an analysis and those who aim to spread knowledge should be careful to describe the world both relevantly and accurately.

With that said, it can be a tough sell if it involves math, even simple math. It's much easier to say that long lenses give you compression, but the problem is that many people will believe it, repeat it, and not know or care that they have a mistaken understanding.