Mark Wieczorek
Jun 29 · 11 min read

Let’s start with the eye.

The eye is — for the purposes of this discussion a sphere. Focused light comes through the lens and reaches the retina where light sensitive photoreceptors turn that light into electrical signals.

When people try to define what a “normal” lens is, they often go back to the human eye — if the eye is what we use to perceive the world, then the eye must be the very definition of “normal.”

This is a slightly flawed argument, but the thought process can lead us to some interesting conclusions.

Angle of View

The first (flawed) argument for human vision being the starting point for what is a “normal” lens is angle of view.

According to Wikipedia, humans can see approximately 210° — or a little more than half of a circle. If you put your arms out to your sides and look forward, bringing them slowly forward until you’re just barely aware of them — they should be basically fully outstretched. Pro tip: wiggle your fingers, your peripheral vision is better at picking up movement than subtle shades of fleshy tones.

Of course this is with two eyes, not one eye, and not all of the image is in focus — indeed we can only see the central portion of what we’re looking at in focus. Plus our eyes move around a lot, even when we’re not thinking about it, they flit from one object to another — completely skipping past all of the area in between.

I suppose we could measure the central area of the fovea — the area with the highest density of photoreceptors, but if 210° was too wide, then this would be too narrow.

Squaring the Circle

The eye is curved. Film is not. Perhaps it’s being curved that’s causing the comparison to fall flat (no pun intended). So let’s square the circle.

Aha! Now we’re getting somewhere. Now the imaging plane (the film) is bounded. The lens must project an image onto a surface whose boundaries are known.

Let’s imagine that this square “eye” is a camera. Let’s use 35mm film as the “standard” here to keep the conversation simple — I’ll expand (again no pun intended) into larger and smaller formats in a bit.

A typical 35mm image is 24mm x 36mm. So we now have a maximum dimension for our image sensor — 36mm.

The Argument for 35mm as “Normal”

Focal Length is literally that. The length of the focus. Imagine a pinhole camera — if you put the pinhole 35mm from the piece of film, you have a 35mm focal length. It’s as simple as that.

Then your next worry is — how big is the film? Well we’ve just defined the film as 36mm x 24mm.

So if you want to “square the circle” you know the the length of one line of the square — 36mm — and you just build a cube of exactly 36 x 36 x 36 and put the pin hole in the opposite end and there you have it — 36mm (rounded down to 35mm) is your normal lens.

Film is 35mm, if you want to mimic the human eye by squaring the circle, you put the pinhole at 35mm away from the film plane and there you have it. 35mm is a “normal” lens.

Problem solved, there’s nothing more to write about. Let’s all go home.

The Argument for 50mm as “Normal”

Actually, lenses project a circular image, not a rectangular image — any rectangular sensor will be a crop from that circle. If we want to actually put the lens as far away from the image as the image is long, we need to calculate the diagonal.

Pythagoras’ little formula a² + b² = c² tells us the diagonal of a 36mm square is 51mm — which we can round down to 50mm.

So perhaps our 35mm cubic box was a little bit too small — we should have built a 50mm box instead.

Yes that’s it — clearly (again no pun intended) 50mm is the true definition of normal. Problem solved, we can all go home safe in the knowledge that 50mm is the true definition of normal. After all, who am I to contradict Henri Cartier-Bresson? Besides, 50mm has a nice ring to it — 50mm. Say it with me — fifty millimeters. Nifty fifty.

The Argument for 43mm as “Normal”

Actually, I totally forgot that 35mm film isn’t square. It’s 3:2 aspect ratio. Those sprocket holes take up a lot of space!

If we want to know the actual imaging circle of 35mm film we need to calculate the diagonal of a 35mm piece of film — which happens to be 43mm.

Just look at how compact and tidy that looks.

Yes, that’s it definitively, case closed, 43mm is the true definition of “normal.” There can be no more argument on the subject. I know you were losing a lot of sleep over this — endless nights spent tossing and turning wondering “Am I truly normal? What are my aberrations? Are they chromatic or spherical? What if I’m not even full frame, what if I’m — gasp — APS-C. Is it possible to be diagnosed as APS-C? I’d better consult the DSM-V. Is there an ICD code for this? Will my insurance cover it?”

No? I’m the only one who wonders about these things? I’m not a camera you say? Nonsense. I see things as they are, complete and undistorted, if that doesn’t make me a camera I don’t know what does.

Circling the Square (and why 43mm is truly “normal”)

There are two more arguments for 43mm being the true definition of normal — at least on a 35mm piece of film.

The Pentax K-1000 and the Epson R-D1.

Image credit: Wikipedia

The Pentax K1000 is the camera I learned photography on — me and countless other student photographers who went out and bought these in droves in their freshmen photography classes. It’s sturdy, all mechanical (there is a battery but it just operates the light meter — you can still take pictures without it), and completely manual. Nothing is automatic, so it forces you to learn the exposure triangle.

When you put a 50mm lens on a Pentax K1000 and have both eyes open — you will see the world from the same perspective. That is — if you’re viewing an object with the Pentax K1000 and a 50mm lens with your right eye, that object will be the same size in your left eye that does not have a camera in front of it.

However — the Pentax viewfinder plays a trick on you. It has a 0.88 magnification. So you’re not truly seeing the 50mm view, you’re seeing (50*0.88 = 44) a 44mm equivalent field of view. Look at that, back to 43mm.

Image credit: Wikipedia

The Epson R-D1 is an APS-C (1.5x crop) sensor camera and is actually the first digital rangefinder, which makes it also the first mirrorless interchangeable lens camera.

If you put a 28mm lens on it it, (28*1.5 = 42) it’s equivalent to a 43mm lens on full frame. Does this lens behave normally? Yes it does.

The Epson R-D1 has a beautiful 1:1 viewfinder — when you look through it you see the world unaffected by distortion. If you have both eyes open, objects are the same size in both.

Being a rangefinder, you are not looking through the lens, instead you get “frame lines” that tell you roughly what area of the scene in front of you the film will see based on the lens you have selected. The 43mm frame lines are large — with your eye against the viewfinder you struggle to see all 4 corners at once. But you can see all of them. This means that the eye does indeed see wider than 43mm.

And that’s the crucial difference. With your left eye open, you can see more of the world than if you just looked through the viewfinder with your right eye. Your eyes aren’t squares, they’re round. They’re not limited by the bounds of the flat back of the box.

So even if 43mm is a pretty good definition of “normal,” we can see 210° with both eyes open — or slightly more than half the world, at least horizontally.

With 43mm on a 35mm film frame, it sees the world “undistorted” — objects projected on to it are the same size that we would see them. However, the 35mm film frame is a “crop” of what the human eye can see because film isn’t round and doesn’t wrap past the corners of the box the way our eyes’ photo receptors wrap around the back of the spherical eye.

If you want to call 35mm, 50mm or 43mm normal — that’s OK. If you want to define “normal” by angle of view, arctangents, or something else — that’s OK.

Me — I’m going to call 43mm normal.

SLR vs Mirrorless

Image Credit: Wikipedia

Remember the focal length is the length of the focus — the distance from the point in the lens where the light rays are focused to the film plane.

Cameras have a “flange-focal distance” — this is the distance between the lens mount and the film plane / sensor.

SLR cameras have a mirror box which causes the flange focal distance to be longer than mirrorless cameras such as rangefinders.

A “wide angle” lens (or a “short” lens) is a lens that is shorter than “normal” and must distribute the light rays along a wider area on the film.

A “telephoto” lens (or a “long” lens) is a lens that is longer than “normal” and just a small portion of the image of the outside world is projected on to the film.

The Canon EF mount is 44mm away from the film plane (isn’t that an interesting coincidence?).

The Nikon F mount is 46.5mm away from the film plane.

The Leica M mount is 27.8mm away from the film plane.

This means that any lens whose focal length is “shorter” (wider) than that, cannot contain the focal length inside the lens itself & some tricks must be played to change this.

Leica has some wide angle lenses that protrude into the camera, effectively moving the lens back closer to the film plane.

Typically, though, if the focal length is wider than what can be contained inside the lens, lens manufacturers must add additional lens elements to bend the light back towards the film plane.

This adds size, weight, complexity and increases the chances for aberrations.

This means rangefinder (and mirrorless) lenses can often be simpler than their SLR equivalents, and since they have to bend light less, typically have fewer aberrations.

The switch from film to digital has also meant that many of these wide angle lenses with a steep angle of incidence (the light hits the film at an angle that’s far from 90 degrees) don’t play as nicely with digital sensors that have additional pieces to them, such as color filter arrays and IR filters.

Judging by the new mirrorless lenses that are coming out, they’re still bending light back towards the sensor to get closer to the ideal 90° angle, but this is just conjecture.

Spherical Aberration

This isn’t something I’d planned on talking about, but while we’re here, it seems as good a place as any to explain Spherical Aberration.

Lenses are mostly made up of “spherical” elements. This means that the radius of the edge of the glass can be described as a section of a sphere. Put another way — imagine a sphere (a globe or something) and then slice a bit off — that bit that you sliced off has a spherical radius — a radius that can be described as a section of a sphere.

Because these elements bend light in an essentially spherical way, when the light hits the film or the sensor, the light itself is spheric — it’s three dimensional. Even objects that are flat in the real world (say, a book — continuing with our map theme, let’s say it’s an atlas).

Because that flat book has been projected through a spherical lens, the center of the book is projected further than the edges of that book — something that’s hopefully made plain in the diagram above.

Val with Leica 90mm f/2.8

This is called Spherical Aberration and it creates a sort of “smooth yet sharp” feeling to images. The edges are sharp and in focus, but the center is subtly out of focus, smoothing out the details.

I own one a few lenses that do this and they yield quite pleasing portraits because of this quality.

Spherical elements are easy to produce — you simply have the glass mounted on one surface and have the grinding (say, sandpaper) element a fixed distance away and you rotate one of them around a fixed point, creating a spherical curve.

The “fix” for spherical aberration is one or more aspheric elements — glass whose radius cannot be described simply as the edge of a curve/sphere. These are, naturally, much more difficult to make, and increase the cost of the lenses.

Aspheric elements were introduced in very expensive lenses some time during the 1970s, but the cost of producing these elements has come down and they’ve found their way into even relatively inexpensive lenses.

The aspheric element is ground into a specific shape so that it counteracts this “the focus is different across a single plane” problem.

Our eyes, of course, solve this in a different way — the rear of the eye is simply spheric itself. Problem solved. There is some progress towards making curved sensors and the speculation is that while this could make lens design easier (no more aspheric elements required) — the lens would have to be specifically designed for that sensor & could not serve as a general purpose lens for any other sensor.

Film / Sensor Conversions

The diagonal of a “full frame” sensor is 43mm.

The diagonal of an APS-C sensor is 27mm (though APS-C sensor sizes vary).

The diagonal of a Micro Four Thirds sensor is 22mm.

The diagonal of a Fuji GFX sensor is 55mm.

The diagonal of a larger Hasselblad sensor (there are several) is 67mm.

Therefore the “normal” lens on each of these sensors would be about that focal length — 27mm for APS-C and 22mm for m43 and so on.

These lenses are typically “pancake” lenses — short lenses that fit close to the body. They can be made small because they don’t have to bend light much and can be made with few lens elements.

The Pentax 43mm f/1.9 (full frame), Fuji 27mm f/2.8 (APS-C) and Panasonic 20mm f/1.7 (Micro Four Thirds) are examples of such lenses — they tend to be smaller than more telephoto or more wide lenses.

Further Reading

What I think about when I think about Focal Length.

Ice Cream Geometry

"The greatest joy for me is geometry" - Henri Cartier-Bresson. "Instagram is all about ice cream and geometry" - Me.

Mark Wieczorek

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Just This Guy, You Know?

Ice Cream Geometry

"The greatest joy for me is geometry" - Henri Cartier-Bresson. "Instagram is all about ice cream and geometry" - Me.

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