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04-12-2010, 09:54 PM   #1
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The Perfect Normal Lens

Quite clearly, the 50mm lens is a very popular focal length on the 135 film and full frame digital format. Unfortunately, it simply isn't a "normal" lens. As far as I am aware of, its origin is from the early rangefinder days when a slightly longer normal lens was popular, and the simple design for the 50mm lens really became easier to develop. Regardless, 50mm just isn't a normal focal length.

Why isn't this the case? A 50mm lens on 35mm film gives roughly a 45 degree angle of view diagonally. So what would be the better normal lens? My guess would be a lens that delivers a 45 degree field of view horizontally. That begin said, it is often believed that the format's hypotenuse is what the normal focal length should be for a given format.

Let's do some calculations. To calculate the diagonal of the format, I will use the Pythagorean theorem, which is a^2+b^2=c^2.

For 35mm film, the dimensions of the film are 36x24mm.

root(36^2+24^2)= 43.2667

Okay, one thing comes to mind here. Pentax actually has a 43mm lens. Awesome! For those shooting 35mm or the mythical Pentax full frame dSLR, the 43mm lens would be the perfect normal lens, assuming the normal lens is the diagonal of the format.

While we're at it, let's calculate the field of view horizontally for 35mm film. To do this using trigonometry, the formula would be 2*arctan(format/2[focal length])

Let's use that to see what the field of view is horizontally for a 43.2667mm lens.

2*arctan(36/2[43.2667])=45.1771

Very close to 45 degrees indeed. But not perfectly so. Why? Well, I'll try a different format, say one with an aspect ratio of 1:1. In that case, why not just keep it simple, and use a format with the dimensions of 1x1.

Using the Pythagorean theorem, I can calculate the diagonal of the format.

root(1^2+1^2)=1.4142

Okay, let's use the formula for field of view to see what the field of view would be for this focal length.

2*arctan(1/2[1.4142])=38.9424

Uh oh. That's certainly not 45 degrees. Isn't that what is apparently the "normal" focal length for this format though? Shouldn't it deliver a 45 degree field of view for the horizontal dimension of the format?

Well, from that knowledge, I can conclude that, assuming the "normal" focal length for a format is that which delivers a 45 degree angle of view horizontally is definitely not that of the diagonal of the format.

By using the formula above, I have come to realize that the perfectly normal focal length of a format is actually a solid value which can be multiplied or divided by the dimension of the desired format to achieve a perfect 45 degree angle of view.

Assuming the normal focal length of a format is that which creates a 45 degree angle of view horizontally on the image, that focal length would be the horizontal of the medium/0.8284, or the horizontal of the medium*1.2071.

Let's put that to the test. For 35mm film, this calculation would thus make a focal length of 43.4558. Oh so close to the diagonal of the format!

2*arctan(36/2[43.4558])=45 exactly

Okay, let's try it with the 1x1 format I mentioned earlier. 1*1.2071=1.2071

2*arctan(1/2[1.2071])=45 exactly

There you have it. 50mm obviously isn't the normal focal length for 35mm film. The diagonal of the format clearly isn't the normal focal length for it. Using trigonometry, I have arrived at the conclusion that the perfect normal focal length of ANY format is that which I showed above.

Enjoy!

04-12-2010, 11:25 PM   #2
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QuoteOriginally posted by Nerdold Nerdith Quote
Why isn't this the case? A 50mm lens on 35mm film gives roughly a 45 degree angle of view diagonally. So what would be the better normal lens? My guess would be a lens that delivers a 45 degree field of view horizontally.
That's an awful lot of math for something predicated on something that's basically just a guess. What makes you think 45 degrees measured horizontally is particularly special?

There's lots of existing threads and existing articles (eg, Wikipedia) discussing definitions of "normal". The most useful definition, IMHO, is that a normal lens would provide a FOV that equals that subtended by a "typical" print viewed from a "typical" distance. This obviously leaves some wiggle room, but at least it gives a reason for preferring a given FOV, as opposed to arbitrarily picking a number (or defining it in terms of the length of the diagonal, which seems equally arbitrary).
04-12-2010, 11:32 PM   #3
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QuoteOriginally posted by Nerdold Nerdith Quote
Quite clearly, the 50mm lens is a very popular focal length on the 135 film and full frame digital format. Unfortunately, it simply isn't a "normal" lens. As far as I am aware of, its origin is from the early rangefinder days when a slightly longer normal lens was popular, and the simple design for the 50mm lens really became easier to develop. Regardless, 50mm just isn't a normal focal length.

Why isn't this the case? A 50mm lens on 35mm film gives roughly a 45 degree angle of view diagonally. So what would be the better normal lens? My guess would be a lens that delivers a 45 degree field of view horizontally. That begin said, it is often believed that the format's hypotenuse is what the normal focal length should be for a given format.

Let's do some calculations. To calculate the diagonal of the format, I will use the Pythagorean theorem, which is a^2+b^2=c^2.

For 35mm film, the dimensions of the film are 36x24mm.

root(36^2+24^2)= 43.2667

Okay, one thing comes to mind here. Pentax actually has a 43mm lens. Awesome! For those shooting 35mm or the mythical Pentax full frame dSLR, the 43mm lens would be the perfect normal lens, assuming the normal lens is the diagonal of the format.

While we're at it, let's calculate the field of view horizontally for 35mm film. To do this using trigonometry, the formula would be 2*arctan(format/2[focal length])

Let's use that to see what the field of view is horizontally for a 43.2667mm lens.

2*arctan(36/2[43.2667])=45.1771

Very close to 45 degrees indeed. But not perfectly so. Why? Well, I'll try a different format, say one with an aspect ratio of 1:1. In that case, why not just keep it simple, and use a format with the dimensions of 1x1.

Using the Pythagorean theorem, I can calculate the diagonal of the format.

root(1^2+1^2)=1.4142

Okay, let's use the formula for field of view to see what the field of view would be for this focal length.

2*arctan(1/2[1.4142])=38.9424

Uh oh. That's certainly not 45 degrees. Isn't that what is apparently the "normal" focal length for this format though? Shouldn't it deliver a 45 degree field of view for the horizontal dimension of the format?

Well, from that knowledge, I can conclude that, assuming the "normal" focal length for a format is that which delivers a 45 degree angle of view horizontally is definitely not that of the diagonal of the format.

By using the formula above, I have come to realize that the perfectly normal focal length of a format is actually a solid value which can be multiplied or divided by the dimension of the desired format to achieve a perfect 45 degree angle of view.

Assuming the normal focal length of a format is that which creates a 45 degree angle of view horizontally on the image, that focal length would be the horizontal of the medium/0.8284, or the horizontal of the medium*1.2071.

Let's put that to the test. For 35mm film, this calculation would thus make a focal length of 43.4558. Oh so close to the diagonal of the format!

2*arctan(36/2[43.4558])=45 exactly

Okay, let's try it with the 1x1 format I mentioned earlier. 1*1.2071=1.2071

2*arctan(1/2[1.2071])=45 exactly

There you have it. 50mm obviously isn't the normal focal length for 35mm film. The diagonal of the format clearly isn't the normal focal length for it. Using trigonometry, I have arrived at the conclusion that the perfect normal focal length of ANY format is that which I showed above.

Enjoy!
.


Rather enjoyed the joke, "Nerdold Nerdith"



.
04-13-2010, 02:06 AM   #4
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Too much Irish Coffee and/or other mood/cognitive enhancers.

Few cams utilizing 135 film had 1:1 aspects. There *were* some (I think the Robot was the most prominent) that used 24x24mm frames, with a diagonal (and thus 'normal' focal length) of 33.9mm, close enough to the popular 35mm lenses. I rather wish I'd had a Robot or the like; 54 shots on a 135-36 cart, yowzah!!

But what's 'normal' for any format / aspect is whatever the camera/lens maker can get away with. With 6x6 cams, the diagonal of the 56x56mm frames is 79.2mm, yet such cams were typically provided with lenses of 75, 80, or 85mm; the equivalent of the 35/FF's 50mm would have been 92mm, rather a short tele.

Recall that 'normal' mathematically is defined as "at right angles to", from norma, the carpenter's square. A right angle is 90 degrees; thus the true 'normal' AOV (angle of view) is 90 degrees, which for 35/FF is given by a 20mm lens, and for APS-C lenses requires a 14.5mm lens. The DA 15/4 or 14/2.8 are thus the most normal lenses for our dSLRs. QED.

Normality is highly overrated. My middle name is Normal. Ay yi yi.

04-13-2010, 02:21 AM   #5
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I found the 50mm lens for 135 film always to be a compromise. I very often used my two "normal" lenses, the 35mm and the 85mm, because the 35mm would app. correspond with my field of vision, if I take in the whole scene, whereas the 85mm lens would correspond to the field of sharp vision, which is the much smaller angle of view, which humans see sharp, when concentrating on intersting parts of the whole scenery.

A often quoted definition for normal lenses, is having a focal length of the diagonal of the film format. That is roughly, what the 40mm pancakes ot the FA 43mm Limited provide (some other manufacturers also made 40mm lenses, like Konica) - but somehow they got never popular, as photogs were (are?) pretty conservative and stuck to the established 50mm fl.

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04-13-2010, 02:41 AM   #6
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Depending on the 35mm system, Lenses were qualified as "normal" with focal length ranging from 35mm (Leica) to 55mm (SLR).

A "normal" length provide perspective that look natural. Speaking of "true" normal lens is nonsense.

On a scientistic perspective, the human eye is a kind of ultrawide low resolution, low contrast system (highly sensitive to movement), added to a high resolution, high color sensitive sensor (the macula) with a hole in the middle (the optical nerve) The reason why we do not see this is that the brain is permantly stiching images and recreating the scene in a sort of "predictive 3D model) How everything works is still not fully understood.

The way a picture works is completly different, you frame a picture, meaning that you choice a porting of space to apply in the picture. This is a choise and weither or not it looks natural depends on the individual usually focal lengthes from 35 to 55mm have such a result.

My own "normal" lens is 43/1.9 (on film), I like it to be slightly wider than 50 but not a true wide angle. I'm confortable with it. But a classic Leica user would say : "A true normal lens is 35mm" as you can see in the X1 (28mm converted with a 1.5 magnification) It depends on the people.
04-13-2010, 07:38 AM   #7
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The perfect landscape lens:



The perfect portrait lens:

04-13-2010, 07:55 AM   #8
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define "normal"

does this mean average? FOr Hunman beings that is not physiologically possible

Same with weather patterns, A lot of time the "normal temperature" is between two typcially occurring ranges one much colder and one much hotter, and normal rarely occurres.

there are a lot of different perspectives on what a normal lens is, and I have used the word perspective deliberately.

For some normal is the field of view, but even with my eyes, that represents almost 180 degrees horizontally and 120 vertically, so I don;t think my 8mm fisheye with 180 degree FOV is "normal"

For some, normal represents the diagonal of the frame, but I have no idea why.

For others, and I believe this the best way to consider things, normal yeilds a photo with the same perspective that someone would get when standing where the photo was taken from. I think for 35mm film that is actually 55-58mm

04-13-2010, 08:25 AM   #9
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The FA 43mm ltd was designed with the diagonal of the 135 film format. That in conjunction with its excellent optics and decent speed make it very close to the perfect lens in the realm of mere mortals.
04-13-2010, 08:49 AM   #10
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I agree with Lowell that "normal" only relates to perspective, not to field of view. But I would say normal is a range, not a number. I call anything from 42-60mm on full-frame a normal lens. Below 42mm is wide, above 60mm is telephoto. Wide angle lenses stretch the perception of depth, telephotos compress the perception of depth, normal lenses render a similar perspective to normal human vision.
04-13-2010, 09:14 AM   #11
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QuoteOriginally posted by audiobomber Quote
. . . normal lenses render a similar perspective to normal human vision.
Since "normal" has been historically used in reference to the perspective of normal human vision, it also has made it next to impossible to assign a number since everyone's eyes are somewhat different. A mean would have to be used. On the other hand, when it is used in relation to the diagonal of the film or sensor, it is mathematically more viable. The F 28mm f2.8 would be a good candidate on the aps-c bodies even though somewhat slow for "modern" normal lenses.
04-13-2010, 09:32 AM   #12
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QuoteOriginally posted by Nerdold Nerdith Quote
Quite clearly, the 50mm lens is a very popular focal length on the 135 film and full frame digital format. Unfortunately, it simply isn't a "normal" lens. As far as I am aware of, its origin is from the early rangefinder days when a slightly longer normal lens was popular, and the simple design for the 50mm lens really became easier to develop. Regardless, 50mm just isn't a normal focal length.

Why isn't this the case? A 50mm lens on 35mm film gives roughly a 45 degree angle of view diagonally. So what would be the better normal lens? My guess would be a lens that delivers a 45 degree field of view horizontally. That begin said, it is often believed that the format's hypotenuse is what the normal focal length should be for a given format.

Let's do some calculations. To calculate the diagonal of the format, I will use the Pythagorean theorem, which is a^2+b^2=c^2.

For 35mm film, the dimensions of the film are 36x24mm.

root(36^2+24^2)= 43.2667

Okay, one thing comes to mind here. Pentax actually has a 43mm lens. Awesome! For those shooting 35mm or the mythical Pentax full frame dSLR, the 43mm lens would be the perfect normal lens, assuming the normal lens is the diagonal of the format.

While we're at it, let's calculate the field of view horizontally for 35mm film. To do this using trigonometry, the formula would be 2*arctan(format/2[focal length])

Let's use that to see what the field of view is horizontally for a 43.2667mm lens.

2*arctan(36/2[43.2667])=45.1771

Very close to 45 degrees indeed. But not perfectly so. Why? Well, I'll try a different format, say one with an aspect ratio of 1:1. In that case, why not just keep it simple, and use a format with the dimensions of 1x1.

Using the Pythagorean theorem, I can calculate the diagonal of the format.

root(1^2+1^2)=1.4142

Okay, let's use the formula for field of view to see what the field of view would be for this focal length.

2*arctan(1/2[1.4142])=38.9424

Uh oh. That's certainly not 45 degrees. Isn't that what is apparently the "normal" focal length for this format though? Shouldn't it deliver a 45 degree field of view for the horizontal dimension of the format?

Well, from that knowledge, I can conclude that, assuming the "normal" focal length for a format is that which delivers a 45 degree angle of view horizontally is definitely not that of the diagonal of the format.

By using the formula above, I have come to realize that the perfectly normal focal length of a format is actually a solid value which can be multiplied or divided by the dimension of the desired format to achieve a perfect 45 degree angle of view.

Assuming the normal focal length of a format is that which creates a 45 degree angle of view horizontally on the image, that focal length would be the horizontal of the medium/0.8284, or the horizontal of the medium*1.2071.

Let's put that to the test. For 35mm film, this calculation would thus make a focal length of 43.4558. Oh so close to the diagonal of the format!

2*arctan(36/2[43.4558])=45 exactly

Okay, let's try it with the 1x1 format I mentioned earlier. 1*1.2071=1.2071

2*arctan(1/2[1.2071])=45 exactly

There you have it. 50mm obviously isn't the normal focal length for 35mm film. The diagonal of the format clearly isn't the normal focal length for it. Using trigonometry, I have arrived at the conclusion that the perfect normal focal length of ANY format is that which I showed above.

Enjoy!
Whatever, dude(ette).
04-13-2010, 09:45 AM   #13
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if people want to understand why a 50mm lens is the "normal" lens, aside from producing images which have very similar perspective to the "normal person" what ever the hell that is, there is one other reason why. This has nothing to do with the eyes, vision, or even the diagonal of the film directly.

Consider that we have a single lens reflex camera. We need to have the shutter in front of the film, and then the mirror, at a 45 degree angle between the shutter and the rear of the lens. The mirror swings up and the mechanism must have room to swing the mirror, and the mechanism must be simple, and very reliable to return the mirror back to the same place time after time, insuring focusing accuracy.

This determines what is called the system regestry, or the distance from the lens mount to the film plane.

Virtually all 35mm SLRs have a regestry of between 42 and 46 mm. (interesting distance, isn't it?)

What this really means, to a lens designer, is that it is very very easy (without computers) to design lenses in this range, with a minimal number of elements, without either extending the light path (as is needed for wide angle lenses) or shrinking the light path (telephoto lenses). WHile keeping the overall dimensions of the lens small compact etc. Just look at pentax's pancake lens line.

In reality I suspect that we can offer a huge number of explanations about comparisons to eye sight etc, but the reality is, normal is normal because it was easy, and cheap.
04-13-2010, 09:52 AM   #14
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Lowell,

We'll have to agree to disagree on the "human perspective" and "normal." How do you explain the fact that most "normal" lenses were originally in the 55mm or 58mm range? With exception of the 50mm f1.4 Super Tak & SMC, Pentax didn't have a 50 in the lineup (excluding the macros) until the k-mount and computer age came along. Some think that Tamron's Adapt-a-matic line was the last non-computer designed lens series by a major firm.
04-13-2010, 09:59 AM   #15
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QuoteOriginally posted by Blue Quote
Lowell,

We'll have to agree to disagree on the "human perspective" and "normal." How do you explain the fact that most "normal" lenses were originally in the 55mm or 58mm range? With exception of the 50mm f1.4 Super Tak & SMC, Pentax didn't have a 50 in the lineup (excluding the macros) until the k-mount and computer age came along. Some think that Tamron's Adapt-a-matic line was the last non-computer designed lens series by a major firm.
see my next post. in the thread, the lens designs were typically ones that were easy to build considering the distance restrictions that the mechancs of an SLR imposed ont he regestry distance.

55, or 58 mm might be the easiest lens to design and make because it is the one that best mounts on a platform 46mm away from the film.
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