# Optics question - eyes and cameras, and the mythical 50mm lens

Eyes and cameras - a topic that has been troubling me
Hi all. This is my first post. I'm seriously thinking about applying to optometric college in the fall. I'm trying to improve my knowledge as much as possible of the area, and one question that keeps coming up (I'm a hobby photographer...) is the difference between the eye and a camera.

Most photographers appreciate that the camera/film eye/retina analogy is only so good, and soon becomes impossible to reconcile with the influence of the brain, not to mention peripheral and foveal vision.

But the problem I'm having is to refute those photographers who blindly state that the eye = a 50 mm lens. I think this statement is nonsense, but I'd appreciate your help to clarify my thinking and back up my arguments.

First, a 50mm lens on a 35mm film camera covers a horizontal field of view of 39.6 degrees. A single human eye, on the other hand, from what I've read gives a field of view of 60 degrees inward, and 100 degrees outward. Though much of that is blocked by my nose. Anyway, the point is that thought of as a lens, the eye's field of vision is much wider than that of a 50mm lens.

I also gather that the foveal central field subtends around 5 degrees (I'm not sure if this is horizontal, vertical, or a solid cone angle), although the central 1/2 degree is the clearest.

So we have two competing views: one is that the human eye has a wide field of view, and the other that we only see a very small part of that clearly.

But neither view helps me explain to friends why the 50mm lens isn't going to replicate human vision: I don't think any lens can replicate human vision. Sure, 50mm lenses normally force people to take pictures (especially portraits) from sufficient distance that they look natural, but that still doesn't explain this obsession with 50 degrees. Furthermore, a 50mm lens on a 35mm SLR, when viewed through the viewfinder, projects an image with the same magnification as we see with our eyes, but this says more about the viewfinder magnification that some inherent property of the 50mm lens.

So you can see why I'm confused, and I would just LOVE to learn a bit more. If anyone has any accurate figures for focal length and viewing angles, and if they can help me understand this whole foveal/peripheral business, that would help me a lot.

Thank you!

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mgb_phys
Homework Helper
First, a 50mm lens on a 35mm film camera covers a horizontal field of view of 39.6 degrees. A single human eye, on the other hand, from what I've read gives a field of view of 60 degrees inward, and 100 degrees outward.
The field of view of the eye is a bit difficult to define - your eye moves around.
But the 50mm focal length (on a 35mm camera) is a little smaller than the binocular fov of one eye.

The 50mm is a bit of a historical accident, it was a convenient size for the new 35mm format. Then as it became established it became the standard lens - so it was generally the best performing lens in a makers line-up because it was the one that people compared with their competitors 'standard' lens.
A couple of makers tried to promote a 40mm as the standard - but they never really caught on

So you can see why I'm confused, and I would just LOVE to learn a bit more. If anyone has any accurate figures for focal length and viewing angles, and if they can help me understand this whole foveal/peripheral business, that would help me a lot.
Good discussion
http://www.luminous-landscape.com/columns/eye-camera.shtml

The "normal" lens for a particular format usually has a focal length that is about the same as the diagonal of the film being used -- for full-frame-35mm that's around 45mm. This is because it's harder to make short wide-field lenses, you may have noticed vignetting on wide-angle photos because the lens doesn't have an even focus or light distribution. Oh, yeah, and spherical distortion too...

It just happens to match up to what we think we see with our un-aided eyes, a kind of balance between wide field and loss of resolution on the edges. The funny thing is that cameras don't "see" the way humans do anyway. We don't notice the fading resolution and depth of field limitations because we scan and re-focus a scene constantly. A realist painting is actually a better re-presentation of a scene than a photograph because the artist "averages" all those re-scans together, more the way we do naturally.

If you really want to tease your photog friends bet that there is no "perspective" difference between a wide-angle and a tele-photo shot taken from the same place. You can prove it by taking both shots and blowing up the wide-angle to match the size of
the tele. It's all about the relative angles. That will really piss them off...

Thanks folks.

Yes - people will swear blind that telephotos compress perspective, and wide angles distort it. It's easy to confuse the so called properties of a lens with the camera-to-subject distance, which is the root of perspective. Also significant is the need to view prints from the correct centre of perspective, and this changes with focal length and print size. Often neglected.

What troubles me most is that, if you can't put a number in mm of the human eye lens, then surely you can reason that it has to lie somewhere on a scale from wide to tele. For example, let's just say I designed an artificial eye that had 10 X magnification. You'd sacrifice field of view for mag, obviously, but imagine the detail you'd see! Likewise, imagine if we made a very very wide angle eye, such that you could see more clearly your eye socket.

If such a continuum is possible, which is surely is, then it begs the question where do we put the human eye on this scale. Surely the eye has a focal length in mm, and this can be scaled up to 35mm equivalent if we know the retina size.

Do we need to flatten the retina first so it's a fair comparison? After all, film and digital sensors are flat, whereas the back of the eye is spherical. That's another spanner in the works.

If anyone's figured this out please put me out of my misery. Thanks

Oh yes - one more thing, thank you schip for pointing out the normal lens. This is a useful measure, but since it's based on a diagonal it doesn't account for aspect ratio. The diagonal of a 4:3 sensor is rather different to that of a 16:9 sensor, even though all lenses cast image circles, not rectangles. Surely it would make a lot more sense to define normal in terms of circles instead of rectangles. Then again, sensors or frames of film aren't circular are they? Hmmmm

...all lenses cast image circles, not rectangles.
Whereas the image sensor is rectangular.

That's an interesting point. Never thought about that before.

Andy Resnick
Thanks folks.

Yes - people will swear blind that telephotos compress perspective, and wide angles distort it. It's easy to confuse the so called properties of a lens with the camera-to-subject distance, which is the root of perspective. Also significant is the need to view prints from the correct centre of perspective, and this changes with focal length and print size. Often neglected.

What troubles me most is that, if you can't put a number in mm of the human eye lens, then surely you can reason that it has to lie somewhere on a scale from wide to tele. For example, let's just say I designed an artificial eye that had 10 X magnification. You'd sacrifice field of view for mag, obviously, but imagine the detail you'd see! Likewise, imagine if we made a very very wide angle eye, such that you could see more clearly your eye socket.

If such a continuum is possible, which is surely is, then it begs the question where do we put the human eye on this scale. Surely the eye has a focal length in mm, and this can be scaled up to 35mm equivalent if we know the retina size.

Do we need to flatten the retina first so it's a fair comparison? After all, film and digital sensors are flat, whereas the back of the eye is spherical. That's another spanner in the works.

If anyone's figured this out please put me out of my misery. Thanks
I waited until responding to the OP, because you are asking a tricky question. The quick answer is that a lens with a 50mm focal length, using the 35mm film standard, provides a normal 'perspective distortion' as compared to the human eye.

That is, although human vision and 50mm images subtend different angles of view, the "depth perspective" of the photograph closely matches the optical properties of your eye. Specifically, the ratio of focal length to image size is similar between the two. For different image sizes, different focal length lenses from 50mm will produce the 'natural' perspective.

The human eye is well-characterized optically: the Gullstrand model is 60 D (most of the optical power is concentrated at the air-cornea interface), the numerical aperture of the eye is around 0.15 (but can vary by adjusting the pupil diameter), and the curvature of the retina helps to eliminate the aberration known as 'field curvature'. Don't get too confused about the difference between fovea and retina- that's a biological adaptation and isn't really relevant.

Don't confuse 'focal length' with the distance from lens to object- the focal length (used in this context) is the distance from the rear principle plane of a lens to the image.

So, longer focal lengths (with fixed image sizes) have different ratios, and so the image will appear to have more or less perspective distortion than 'normal' vision.

Now, this is all different from magnification and resolution- one can magnify an image (nearly) arbitrarily large, but one generally *cannot* increase the resolution an arbitrary amount- the resolution is related to the ratio of the diameter of the pupil to the focal length, while magnification is related to the ratio of front and back focal lengths.

Does this help?

turbo
Gold Member
When I was shooting portraits for class pictures (35mm film) I would use 50mm on the guys quite often, but would default to 100mm+ for the girls. The longer focal length flattened facial features, and combined with with a "soft" filter and multi-directional lighting, gave portraits that were quite popular with the subjects.

After moving up to Bronica medium-format cameras (etr-series), I kept the same philosophy going (normal lenses and directional lighting for the guys, mild telephotos and multi-directional lighting for the girls) - it worked well.

Furthermore, a 50mm lens on a 35mm SLR, when viewed through the viewfinder, projects an image with the same magnification as we see with our eyes, but this says more about the viewfinder magnification that some inherent property of the 50mm lens.
You have to look a little closer. Regardless of whether the gross image is the same size, do near objects scale the same as distant objects? It's a matter of perspective, not magnification. When I normally take in a view that includes several faces, I don't expect the noses to be significantly closer to me than the ears.

If looking through the viewfinder with one eye and around the camera with the other, ultimately you have the same perspective in both cases (the distance to subject) and are controlling only the field of view onto the image area. To look natural, you want to hold the photo in its finished size at normal reading distance, and imagine looking "through" it to trace the scene. That will vary based on your distances. Notice that you are not considering the total field of view of the eye; just the part that intersects the frame.

IMO, 50mm is not quite natural looking. 55 is more like the correct answer.

Hmmm, thanks folks. I'm getting conflicting messages. One thing is absolutely clear. Focal length doesn't impact perspective. Not one bit.

The reason people tend not to use wide angles for portraits is that, to fill the frame with the subject's head and shoulders, a wide angle would force you to stand very close to the subject. Likewise, to fill the frame, a telephoto would require the photographer to stand back.

This act of moving closer or further from the subject determines perspective. The perspective imaged by a wide angle or a telephoto lens from the same position is exactly the same. It's just one covers a different field of view than the other.

As for the looking through the viewfinder trick, you can adjust the focal length (if you had a zoom lens) until objects in the real world appeared the same size as they do in the viewfinder. But this tells you nothing about the human eye, because different viewfinders have different magnifications. So it's something of an arbitrary comparison, I think a lot of people take the viewfinder image as a given, whereas in fact the optics in the prism determine how large or small objects appear.

In that regard I don't understand how 55mm is more eyelike than 50mm, but I do appreciate your efforts to help me understand. I don't mean to be difficult or argumentative, but the points about perspective above are common myths, and luckily Anselm Adams covers them in his book "The Camera"

That is, although human vision and 50mm images subtend different angles of view, the "depth perspective" of the photograph closely matches the optical properties of your eye. Specifically, the ratio of focal length to image size is similar between the two. For different image sizes, different focal length lenses from 50mm will produce the 'natural' perspective.
Thanks for your input, but I confess I'm a little confused. The 'depth perspective' is governed by the camera position, not focal length. Changing focal length while standing in the same spot does not alter the perspective: angles to objects in the scene are identical, as are relative sizes.

As you alter focal length, though, the projection centre changes. This means that for a wide angle pic you should either print it larger or stand closer to it, and for a telephoto you should stand further away or print it smaller. When prints from different focal lengths are printed at the same size and viewed from the same distance, it's inevitable that some look right and others look wrong, ie not natural. Perhaps this is what you're hinting at.

turbo
Gold Member
Hmmm, thanks folks. I'm getting conflicting messages. One thing is absolutely clear. Focal length doesn't impact perspective. Not one bit.
That is exactly wrong. If you want a person's face to subtend the same angle on the negative and you shoot the subject with a short lens, their nose will be horribly large on the image. Use a normal lens, and the prospects improve. Use a moderate telephoto lens, and you get a much more attractive result.

Just did a little experiment with my half-frame Nikon D200 and a zoom lens. It looks to be about a 55mm zoom to get a one-to-one image in the viewfinder and with the bare eye. This would be a 110mm on a full-frame camera, which ?coincidentally? is about what is recommended for portraits minus the large noses....

http://www.clarkvision.com/imagedetail/eye-resolution.html

Now we can start discussing death-of-field and circles-of-confusion?

That is exactly wrong. If you want a person's face to subtend the same angle on the negative and you shoot the subject with a short lens, their nose will be horribly large on the image. Use a normal lens, and the prospects improve. Use a moderate telephoto lens, and you get a much more attractive result.
I'm afraid I am totally right, and my position is backed up by all the reputable photography books. Unfortunately there are 100s of less reputable photography manuals that give advice such as "use a 135mm for portraits because it will make noses look more flattering"

That is 100% wrong. The reason noses look unflattering is because if you stand very close to someone's face, the distance from nose to ears as a proportion of the distance from camera to nose is very big.

If you step back a few metres that proportion decreases dramatically. Now, if you stand well back and take the portrait with your wide angle lens, the perspective will be flattering. Why? Because perspective is defined by subject to camera distance. Not focal length.

You may argue that if you used a wide angle from some distance the subject would appear very small. And you'd be right. But if your lens was good enough, and you had enough megapixels, you could crop out the central portion of the frame and you'd see identical perspective to the same shot from the same position using a longer focal length.

I used to believe the nonsense that telephoto = flattering, wide angle = unflattering. It is totally 100% wrong, but unfortunately a lot of people don't understand it. I can see how there is a link between focal length and perspective, in that certain focal lengths force you to move closer or further from a subject. But to claim that focal length is the cause of that relationship is beyond reproach. It's camera to subject distance that matters here.

Luckily perspective is one thing I know about.

However I'm still ignorant about the human eye / camera focal length comparison, and I'm willing to admit that ignorance and hopefully learn a thing or two!

Just did a little experiment with my half-frame Nikon D200 and a zoom lens. It looks to be about a 55mm zoom to get a one-to-one image in the viewfinder and with the bare eye. This would be a 110mm on a full-frame camera, which ?coincidentally? is about what is recommended for portraits minus the large noses....

http://www.clarkvision.com/imagedetail/eye-resolution.html

Now we can start discussing death-of-field and circles-of-confusion?
But if your D200 had different viewfinder prism with different magnification, this experiment would be worthless wouldn't it? Viewfinders come in different shapes and sizes, some have different coverage and magnification. I submit that matching the real world to the viewfinder tells you more about your viewfinder than it does about human vision. The viewfinder magnification is arbitrary. I have 35mm cameras with different viewfinder magnification.

mgb_phys
Homework Helper
Because perspective is defined by subject to camera distance. Not focal length.
But for a given image size - subject distance and focal length are related.
So a wide angle lens close up does give a different perspective to a long focal length lens from further away - it's rather hair splitting to say that since this is due to the distance not the focal length then the lens has no effect.

But for a given image size - subject distance and focal length are related.
So a wide angle lens close up does give a different perspective to a long focal length lens from further away - it's rather hair splitting to say that since this is due to the distance not the focal length then the lens has no effect.
But how? The reason this confusion is so widespread is because people misattribute perspective effects to the focal lenght of the lens. If people were to realise that camera-subject-distance affects perspective, not focal length, then the world would be a better place.

It is 100% to do with distance. I don't see how that's pedantry. The lens has zero effect on perspective. If the photographer decides that they need to move closer or further from a subject then that will change perspective, and you could argue that a choice of lens may force the photographer to move forwards or backwards in order to fill the frame. But that is still the photographer deciding perspective, not the lens.

Very few people appear to appreciate that distinction, I really don't think it's splitting hairs because it's such a fundamental misunderstanding...it goes well beyond the realm of pedantry in my opinion.

The acid test is always to crop the central portion from a wide angle shot. The perspective will always be the same as a longer focal length shot from the same position. Always always always*

*assuming your lens doesn't have some kind of nasty distortion which would invalidate the test.

Andy Resnick
Thanks for your input, but I confess I'm a little confused. The 'depth perspective' is governed by the camera position, not focal length. Changing focal length while standing in the same spot does not alter the perspective: angles to objects in the scene are identical, as are relative sizes.

As you alter focal length, though, the projection centre changes. This means that for a wide angle pic you should either print it larger or stand closer to it, and for a telephoto you should stand further away or print it smaller. When prints from different focal lengths are printed at the same size and viewed from the same distance, it's inevitable that some look right and others look wrong, ie not natural. Perhaps this is what you're hinting at.
I think you are entirely missing the point about *image size*. Enlarging (or shrinking) an image is completely different than the original image size produced by the lens.

Depth perspective has *everything* to do with the lens. It may help you to see what tilt-shift lenses do. Depth perspective is a form of distortion- the variation of magnification with object height. The only lenses lacking depth perspective (and not coincidentally have negligible distortion) are telecentric lenses. Long-focal length lenses have less distortion than our eyes, short focal length lenses have a larger distortion.

http://en.wikipedia.org/wiki/Perspective_distortion_(photography)

I think you are entirely missing the point about *image size*. Enlarging (or shrinking) an image is completely different than the original image size produced by the lens.

Depth perspective has *everything* to do with the lens. It may help you to see what tilt-shift lenses do. Depth perspective is a form of distortion- the variation of magnification with object height. The only lenses lacking depth perspective (and not coincidentally have negligible distortion) are telecentric lenses. Long-focal length lenses have less distortion than our eyes, short focal length lenses have a larger distortion.

http://en.wikipedia.org/wiki/Perspective_distortion_(photography)
There is no such thing as variable depth perspective due to a lens. All standard rectilinear lenses record perspective in exactly the same way a human eye does. Telephoto lenses do not 'warp' perspective. This is not a form of distortion. It is basic geometry and angles that define why near things appear bigger than distant things. This has been well understood since the 1400s. Are you suggesting that you've discovered a new rule of geometry? Our eyes, or lenses, do not exhibit perspective distortion. Neither does a pinhole camera. They may exhibit lens distortion such as pincushion or barelling, but there is no such thing as perspective distortion. Linear perspective is well explained and very predictable.

The type of 'distortion' you may be alluding to is purely psychological, and results directly from viewing a photo from a place other than its true centre of perspective. A photograph taken with a wide angle lens needs to be viewed closer (or printed larger) than a photograph shot with a normal lens. If you view the wide angle shot from the same point (and the same print size) as the normal lens shot then things will look funny because you'll be viewing it from behind the image's centre of perspective. To learn more about this I suggest you consult Rudolf Kingslake's excellent "Optics on Photography" you can read the whole first chapter here http://books.google.com/books?id=hc...ticsin photography&pg=PA1#v=onepage&q&f=false

Tilt shift lenses alter the angle of the image plane. Thus you can avoid the convergence of parallel lines (eg of a skyscraper) by adjusting the orientation of the image plane at the back of the camera. That is an exception, but you are right to point it out. Therefore we can say that tilt shift lenses affect perspective. Good point.

Non tilt shift lenses, however, do not exhibit this strange perspective depth effect that you invoke. There is no such optical effect. It is merely a consequence of the viewing environment.

If you are right, that somehow lenses of different focal lengths 'warp' perspective differently, perhaps we should be able to observe this effect by shooting a rectangular grid. Presumably the telephoto will warp the image in a different way to the wide angle lens, is that what you're suggesting?

Other good books for the perspectivally unenlightened are "The Camera" by Anselm Adams and "Amphoto guide to lenses" by Keith Bancroft.

Both spell out very clearly that the compelling idea of perspective distortion is a myth, and highlight the importance of a picture's centre of perspective. It is for this reason that folks sitting in the front of a cinema will get a very different experience to those sitting in the back. It has nothing to do with lens distortion.

It is ironic that I came here looking to understand an aspect of optics about which I knew (and still know) very little, but have ended up spending all my time explaining basic perspective to some of the resident experts.

Per viewfinder issues.... of course. But I would assume (you know the ***-of-me bit) that the magnification is in the 1::1 region. It was just interesting that it appeared to be about twice the "normal" focal length.

To the perspective point... The quoted text:
Because perspective is defined by subject to camera distance. Not focal length.
is exactly correct. Perspective and camera distance go hand in hand. Focal length is a kludge to match resolution to the size of the image you want. If you had infinite resolution, sharpness, and un-distortion (is there such a thing?) you could shoot with an ultra-wide-angle lens from Long-Island and just blow-up the bit you were interested in to get that Moon-over-Manhattan perspective you like.

None of this is answering the OP's original question about the focal length of the human eye, but I think that link I gave a while ago took a stab at it.

Hmmm. And what is double confusing is that viewfinder magnification is expressed in terms of a 50mm lens. So 1x doesn't mean 'neutral mag' it just means it matches a 50mm lens. Manufacturers tend not to scale this is for 1.6 x crop bodies, so take any specification with a large grain of salt.

jtbell
Mentor
I put my camera on a tripod and set up a scene with a desk lamp about 0.6 m away, and a painting on the wall about 2.5 m away. I took two shots with the lens zoomed to focal lengths of about 24mm and 75mm. This is with a Nikon D80 that has a sensor a factor of 1.6 smaller than 35mm film, so its "normal" focal length is about 35mm.

The original picture shot at 24mm of course has a much wider field of view. I cropped it in Photoshop to match the other one fairly closely for comparison, and scaled both of them to the same size. The relative sizes of the lamp and the painting are almost the same in both pictures. I think the small difference is related to the fact that the front of the lens moves about 40 mm when I zoom between the two focal lengths, so the effective location of the camera is probably slightly different in the two pictures.

The 24mm shot does have greater depth of field (the lamp isn't as blurred), and it shows more image noise because I had to enlarge it by a factor of about 3x before cropping it. (I set the camera to ISO 800 so I wouldn't have to use flash, so there's much more noise than I normally get in pictures from this camera.)

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turbo
Gold Member
There are people here talking past each other. When you have to capture a subject and you want the image to subtend a reasonable angle at the focal plane (a critical part of composing your subject), you have to choose your focal length and distance to accomplish this. If you try to create a portrait of a person with a 28mm lens, the person's face going to be very distorted. You can preserve perspective by shooting the portrait from very far away, but that surely ruins the concept of shooting portraits because the subject's image will be very small on the film. There goes the composition.

In the days of film photography, photographers were constrained by film speed and film grain, and there were limited choices of emulsions. Creating attractive images with such gear meant choosing focal lengths and subject distances that would minimize the distortions caused by perspective. There are related constraints today, but those have been softened a bit by digital cameras' ability to change ISO. Still, you can't take an image of a distant object with a short focal length and enlarge it with sufficient quality to approximate the quality and lack of perspective distortion that you can achieve with a longer focal length.

Exactly. I agree. Now you can see why it's nonsense when people confound focal length with 'flatteringness'. Experienced photographers (who really should know better) will swear blind that you simply can't shoot a portrait with a wide angle lens, no matter what. They attribute some mysterious perspective distortion characteristic to wide angle lenses.

They of course talk rubbish. Wide angle lenses see the same perspective as telephotos. To claim otherwise makes no sense. Perspective is controlled by your feet, not your lens. Your lens may influence where you put your feet, so there is an association, but there is no inherent optical causality between focal length and perspective. Many will swear blind that there is.

"Hmmm, thanks folks. I'm getting conflicting messages. One thing is absolutely clear. Focal length doesn't impact perspective. Not one bit.

That is exactly wrong. If you want a person's face to subtend the same angle on the negative and you shoot the subject with a short lens, their nose will be horribly large on the image. Use a normal lens, and the prospects improve. Use a moderate telephoto lens, and you get a much more attractive result."

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