The Human Eye - Our Prime lenses

in Academic
By sachin/Sachin (1,108) Send mail to this user on September 19, 2002 9:36:50 PM CDT

Trivia of the Eye
Calculations Of Focal Length, Aperture
Why is 50mm lens "normal" for 35mm film?
Seeing in Seeing. "Normally" speaking.
Other Lenses
Acknowledgments and Disclaimers


I am neither an optometrist nor a doctor. But I can surf the web when I am curious. Through this article I wish to share with you the information I garnered from the internet.
The human eye has been touted as the pinnacle of evolution. One of the most complicated part of the human anatomy. It provides us with one of the senses. This sense of sight is perhaps key to human survival since humankind and its ancestors first roamed this planet.

In this article, I will try to compare the human eye, with the second most important tool of the photographer. The Lens.
I will recite interesting trivia and when necessary, boring equations. I will digress and briefly meander through my assumptions about the evolution of the human eye and in the end, talk a little bit about the other lenses.

This article is geared more towards newer entrants into the field of photography. Experianced photographers CAN find interesting trivia or answers to questions they never asked themselves.


Trivia of the Eye

  • The maximum aperture of a cat's eye is about f/0.9
  • The maximum aperture of a human eye is about f/2.1
  • The minimum aperture of a human eye is about f/11 or f/8.6
  • The focal length of a human eye is about 17.2mm (It varies from person to person like all information given here)
  • The ASA of the retina is higher than most films produces today. Infact a few dozen photos can be registered by the eye through the retina. Take that Fuji! Take that Kodak!
  • The colors are captured by cone-shaped cells in the eyes while the intensity is measured by rod-shaped cells.
  • Rabbits are far-sighted. That's why they get scared of airplanes flying far in the sky. Evolution's way of keeping rabbits aware of hawks and other high-flying predators!
  • Rabbits have almsot 360 degrees of field of vision. They can almost see what's happening behind their heads!
  • Some birds have monocular vision. What they can see with one eye, they cannot see with the other(just like the rabbits). This way they can see more of their environment and look out for predators or prey.
  • Raptors (hawks, eagles) have binocular vision, like us humans. There is a large overlap between the fields of vision of both the eyes. This helps them to see a sharper image (also helps in calculating distance).


Calculations Of Focal Length, Aperture

Some of my reasoning about the human eye's focal length:
According to the Magill's Medical Guide Revised Edition; Brain. Salem Press, 1998: 608, the human eye measures about 24.5 mm from the front to back. So all the light that enters the human eye, has less than 24.5mm to converge to a focus. That is, parallel light rays, have less than 24.5mm to convrege to a point. So the human eye's focal length, has to be less than, or equal to, 24.5mm. Are you still with me?:)
We will now look at more hard facts, and emperical data from our trusted optometrists to calculate and understand the focal length of the eye.

To understand the focal length, we must first understand what the Diopter value of the eye is.
Diopter value refers to the refractive power of a lens. The refractive power of a lens, ability of a material to bend light, depends on the curvature of the lens.
A '1 diopter lens' will focus (parallel) light from infinity at a distance of 1 meter behind the lens
Diopter = 1 meter / (Focal Length)
Focal Length = 1 meter / Diopter Value
Some of us know from common popular knowledge how lenses look in general. Fisheye lenses are more curved, and large focal length lenses are almost, if not definitely, concave.
Fisheye lenses are very convex == smaller focal length.
The eye is also shaped like a ball. Hence it must also have a small focal length, like a fisheye lens or a wideangle lens.

Your optometrist will tell you that the human eye generally has a diopter value of 58 or 59.
focal length = 1 meter/58 = 1000mm /58 = 17.24mm
If the diopter value was 59, then following the same calculation, the focal length would be about 16.9mm. As you see, the human eye's focal length is about 17mm, which is withing the 24mm limit set by the size of the eye.
So why don't we see everything as we expect to see form a wide-angle or a fisheye lens? For that you will have to read the next section to find an answer beyond the obvious "Because our sensors are not in the 35mm format:)"

The maximum diameter of the pupil (the hole through which light enters the eyeball and proceeds to the retine) is about 8mm.
Aperture is denoted as f/(a number), where f is the focal length.
So in our case, f = 17, D = 8, aperture = 17/8 = 2.125.
Therefore the aperture of the human eye can be denoted to be about f/2.1
Aperture and focal length given here are not necessarily the same for all people.


Why is 50mm lens "normal" for 35mm film?

This is the question that started my quest for answers!

Why is 50mm lens called as a "normal lens" for 35mm format?
Why is 75mm (or 80mm) lens called as the "normal lens" for medium format?

I quickly realized an intriguing relationship between the format of the film and the supposedly normal lenses.
The focal length of the normal lens, is almost equal to the diagonal of the format of the film.
For 35mm:
Dimensions of the film = 36x24 (mm)
Diagonal of the film = ((36x36)+(24x24))^0.5 = 43.266 (mm)
For 6x6:
Dimensions of the film = 60x60 (mm)
Diagonal of the film = ((60x60)+(60x60))^0.5 = 84.852 (mm)
For 6x4.5:
Dimensions of the film = 60x45 (mm)
Diagonal of the film = ((60x60)+(45x45))^0.5 = 75.00 (mm)

So you see. There is something about the normal lenses which requires their focal length to be about the same as the diagonal of the film!

Silvio Bacchetta (a member of PhotoSIG) explained to me that focal length is not the character that distinguishes a normal lens from a wide angle and zoom lenses. I was skeptical at first. But when I thought more about it, it made sense!
After all, why do we have a "wide angle lense" and not a "short focal length lens"? As Silvio put it, "Photographers are stuck with the concept of focal length!".
But the real world is looking in terms of angles. Think about it. We have a focal length of 17mm. That is a wide angle lens. In fact we DO SEE with a set of wide angle lenses. But our attention is selective in that we instinctively concentrate on a small portion of what we see. In other words, we don't notice all that we see. This is exactly what Kevin Connery (another PhotoSIG member who came to my rescue and answered this question) said in terms of focal length.
Humans, being predators and prey (since prehistoric ages) needed to look out for themselves. They needed to know if a tiger, or a Lion, was lurking beside them. They needed to see as much as possible. Hence we have a wide angle view. But simultaneously, being the predators too, we needed to cencentrate on a small portion of what were were seeing. We needed to understand a situation munutely, in order to manipulate it for our own survival and triumph. Hence we have a binocular vision and are able to concentrate on a small portion of what we actually see!
The moment the prehistoric man noticed something "from the corner of his eye", he had a choice of turning his head to concentrate on the new development. Perhaps because our brains were growing bigger, evolution made it possible for us (and other higher mammals) to be able to move our eyeballs in the sockets. Most creatures below the evolutionary ladder cannot move their eyeballs in the sockets.

So coming back to the lenses and human eye....we infact should compare the eye and a normal lens in terms of solid (conical) angles rather than linear distances.

Then why is 50mm considered the normal lens and not 45mm, as the calculations show?
I didn't find any hard evidence to the reason. But again I found interesting pages on the internet citing opinions which sounded plausible and I will recite them here.
In older rangefinders, supposedly the standard lens was 45mm. But as SLRs were developed, the reflex mirror was introduced into the camera body. To provide space for the mirror, manufacturers needed a lens with less corvature than a 45mm lens. As discussed previously, as the focal length of a lens decrease, the curvature increases. And thus a 50mm lens became the standard for 35mm format.


Seeing in Seeing. "Normally" speaking.

On a 35mm film, a 43.2mm lens will create an image most similar to what we observe with our naked eyes.
Is it true in all cases?
In fact, NO!
When you see a 4"x5" print, of a 35mm negative, shot with a 43.2mm lens, do you always expect it to be exactly like it would be if you saw it in real life?
If you held the 4x5 print, 10 feet away from your eyes, does it look natural?
Obviously Not!
Why? Because our angle of vision now include many extraneous objects that tend to fight for attention along with the print.
If you held the 4x5 print, 1" away form your eyes, does it look natural? Again the answer is NO.
This time we are not looking at the complete picture. Our angle of vision does not encompass the whole print.

When you hold a 4x5 print, from a distance of about 6.5" you will appreciate the picture the most. I gaurantee it:)
Why? Because humans have a cone of visual attention of about 54 degrees. This too varies from person to person, but usually it is between 35-55 degree. So when you hold a 4x5 print at a distance of 6.5" your attention is spread all over the picture without including too much of other information. The picture fills your cone of attention.
In the same way, a 43.2mm lens will subtend a 53 or 54 degree angle on a 35mm film, creating an image most similar to the human experiance, when the image is viewed from a distance equal to the diagonal of the medium, that is when the angle subtended is about right.
That is the concept of the "Normal Lens"!


Other Lenses

We need the other lenses to add more to the "normal" picture.
The invention of a camera was more of an scientific achievement. The camera was intended to record a moment of time. So a 45mm lens would do just fine.
But to have more impact, additional lenses become necessary in some situations. To capture the expression on a football players face. To capture the picture of a yawning tiger. To express the vastness of a staircase. For these instances, a normal lens capture just the reality and not an additional implied meaning or impact. For this zoom or wide angle lenses are necessary.
I consider the wide-angle, fisheye and telephoto lenses (to some extent) more as tools to enhance the artistic nature of the picture rather than to capture the scene as it existed at a point in time, as seen by people involved.

Both wide-angle and telephoto lenses create additional variables for a photographer to play with.

  • Intrinsically zoom lenses have shorter (or shallower) depth of field (DOF) and wide angle lenses have larger DOF.
  • The sense of depth is better conveyed through a wide angle lens rather than a telephoto lens, which tends to compress the view, making it more 2-dimensional in its look.
  • Edge distortion is more evident and possible in the wide angle lens.
A photographer can use these qualities to his or her own advantage, to convey a specific idea or feeling.


Acknowledgments and Disclaimers

Many thanks to Silvio Bacchetta for explaining the concept of the angle of vision, to Kevin Connery for explaining to me in terms of focal lengths, and to Craig Chapman for explaining about the perspective.

Many thanks to the U.S Department of Defence for investing and creating the Internet. Inspite of their original ambitions, the internet has served me well to quench my thirst for knowledge.

I hope you enjoyed reading this article and learned something interesting. If you like it or dislike it, agree or disagree with something, I hope to get both positive and negative comments from you (hopefully with some explnation:)





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