Sensor size v Pentax focal lengths

**wizofoz** · 10-05-2010, 10:18 PM

Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians?

Is there any relationship to sensor size and square/square root factors? i.e. 31 x 1.4 = 43.4. 50 x 1.4 = 70, 55 x 1.4 = 77

Is there anything here to explain the unique Pentax focal lengths?

(P.S. I'm not sure if this is correct forum, so please feel free to move it)

Mikheil88 · 10-06-2010, 12:14 AM

As long as I know sensor size (physical size) affects image quality. e.g. full frame sized 12MP sensor would produce better image than aps-c size 12MP sensor. But I know nothing about focal lenght affections.

wlachan · 10-06-2010, 12:25 AM

Originally posted by wizofoz

Tell me I'm crazy

Okay you are crazy.

**wizofoz** · 10-06-2010, 12:59 AM

Originally posted by wlachan

Okay you are crazy.

Thanks, I needed affirmation!

WerTicus · 10-06-2010, 01:35 AM

probably done to help you choose lotto numbers.

Hypocorism · 10-06-2010, 01:42 AM

Originally posted by wizofoz

Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians?

Is there any relationship to sensor size and square/square root factors? i.e. 31 x 1.4 = 43.4. 50 x 1.4 = 70, 55 x 1.4 = 77

Is there anything here to explain the unique Pentax focal lengths?

Well, Britain has now formally recognised Druids as a religion, so that might have something to do with it.

But seriously, yes of course you could derive many mathematical equations from the extensive range of lens focal lengths and other mfgr specs of camera components, but don't forget to account for the mythical anticlockwise vortex of draining water in the southern hemisphere and that the sun only ever rises on days that end in y.
Then apply Fermet's theorem to the result and see what you get. I predict it should be mind numbing.

But as we all secretly know, the underlying problem is that Pentax designers all must smoke funny weed which accounts for why only Pentax ends up producing such weirdo non-conformist focal length sizes like 31mm, 43mm, 77mm etc. with equally weirdo f/stops like 1,9, 2.4, 3.2 ad infinitum.
(the mere thought of rounded numbers for simplified market understanding and sanity completely escapes them for some reason)

And I also suspect that they plan a fixed 666mm zoom lens for the future, just to show Canikon who really rules the game - but don't quote me on that.

Fwiw: The fear of the number 666 is known as hexakosioihexekontahexaphobia.
(in case you might want to know that bit of trivia.

Hope that answered your question, or at least confused you as much as you've confused everyone else with the enigma of your original post.

dlacouture · 10-06-2010, 02:09 AM

Well, 43mm is the only focal length that actually makes sense, as it's the true normal length of 24x36 (it's the diagonal of a 24x36 rectangle).

Spongefingers · 10-06-2010, 02:12 AM

Originally posted by wizofoz

Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians?

I don't think your numbers are quite in order.
Don't you mean it like this:

FF 135
36x24 diagonal = 43.3

APS-C (Px/Nk/So)
23.6x15.7 diagonal = 28.4

APS-C (Canon)
22.2x14.8 diagonal = 26.7

4/3rds
17.3x13 diagonal = 21.6

645 (1.3x crop)
44x33 diagonal = 55

645 (FF)
56x41.5 diagonal = 69.7

120 (square)
56x56 diagonal = 79.2

These numbers are indeed quite telling.
Supposedly, a 43mm lens will have the same field of view on a 135 frame as a 70mm would have on a 645 frame, but it's never precisely the same.

Originally posted by Hypocorism

But as we all secretly know, the underlying problem is that Pentax designers all must smoke funny weed which accounts for why only Pentax ends up producing such weirdo non-conformist focal length sizes like 31mm, 43mm, 77mm etc. with equally weirdo f/stops like 1,9, 2.4, 3.2 ad infinitum.
(the mere thought of rounded numbers for simplified market understanding and sanity completely escapes them for some reason).

I figured it was because they may be more honest about the optical formulas than other companies. Also, it could be considered as an extra dimension of individuality in such desirable designs.

**wizofoz** · 10-06-2010, 05:07 AM

yeah ok, so I'm looking for meaning where there is none. Obviously a slow day in the office...

Oh and Hypocorism, thank you for your most elucidating reply. I cackled all the way through.

...and I like being enigmatic (and sometimes totally off the beam)

Thanks for the corrections spongefingers, I had rounded the numbers, and gotr one totally out of whack.

Thinks I need me some more of that funny weed.

RioRico · 10-07-2010, 10:02 AM

There's a simple explanation for the progression: the square root of two, ~1.4.

A 135/FF frame has ~twice the area of an APS-C or 135/HF frame, which has ~twice the area of an m4/3 frame; just as an f/1.4 iris opening has twice the area of an f/2 opening, which has twice the area of an f/2.8 opening, etc. Those frame diagonals are actually the diameters of the image circles needed to cover those frames. To double a circle's area, multiply the diagonal | diameter by the square root of two, ~1.4. No magic, no coincidence, just geometry.

A more telling progression is that of common focal lengths. Here is a table of that progression, and the ratios:

012mm 0.00 (like my Vemar 12)
016mm 1.33 (like my Zenitar 16)
021mm 1.31 (like my Tokina 21)
028mm 1.33 (like any 28)
037mm 1.32 (like my Mir-1)
050mm 1.35 (like any 50)
065mm 1.30 (there's a hole here)
085mm 1.31 (like a portrait 85)
105mm 1.24 (like a macro 105)
135mm 1.29 (like any 135)
180mm 1.33 (like my Meyer 180)
240mm 1.33 (like my Enna 240)

If we go from 55 to 70mm, the ratio is... 1.27, close to the above ratios. Each common focal length is roughly 1/3 longer than the previous shorter FL. This suggests that changing the FL by ~1.3 gives a different enough AoV | FoV to serve a different purpose.

Parallax · 10-07-2010, 10:32 AM

Your math is correct, but image circle and focal length are not the same thing. If they were lenses shorter than 28.4mm would not work. The 16-45 for example, would have one serious vignette problem at 16mm!

To the OP: It has been a long held theory by some that a lens with a FL equal to the film (sensor) diagonal produces an image that looks most like what the eye sees.
This was the apparent philosophy behind the FA43mm.

RioRico · 10-07-2010, 08:14 PM

Originally posted by Parallax

Your math is correct, but image circle and focal length are not the same thing.

I never said they were, just that doubled frames and doubled apertures follow the same geometrical rules re: the square root of two.

[/quibble]

Class A · 10-09-2010, 01:23 PM

Originally posted by wizofoz

Is there anything here to explain the unique Pentax focal lengths?

Yes, as other's explained 43mm was chosen because it results in a real normal lens. The common 50mm is a bit too long for 35mm film with a 43.3mm diagonal. BTW, this is not based on a "theory". It is a physical fact that an image viewed at the distance of the image diagonal (commonly regarded as the natural viewing distance) will show a scene with natural angles if the image was taken with the focal length of the sensor/film diagonal.

Regard the 77, the designer Hirakawa wrote that they knew that a good focal length for portraiture had to be between 70mm and 80mm and that they finally went for 77mm because "77" is a lucky number in Japan.

I don't know any story about the 31.

brecklundin · 10-09-2010, 09:36 PM

fyi rumor has it, the dude, Hirakawa, who designed the 43ltd, 77ltd and a bunch of other classic Pentax glass has apparently been asked to take his lunch break elsewhere, retired, kicked to the curb, pick your most salacious terms and insert here....

Maybe he will go work for Canon since his cohort in that period of lense design is apparently now with Nikon...so they could compete head to head so to speak. Or the guy is gonna take his cash and enjoy life at just 48yrs old...lucky bastage!! Nothing but golf and Hello Kitty Porn...

Personally I think the pink K-r lenses and bodies broke the guy...I mean a person has to have limits, right? And the thought of a camera with Notre Dame of, almost as bad, 'Frisco Junts (San Francisco Giants for those w/o a sense of humor) colors on a camera make me wanna buy a sledge hammer and a blow torch!!

Class A · 10-10-2010, 01:23 PM

Originally posted by brecklundin

fyi rumor has it, the dude, Hirakawa, who designed the 43ltd, 77ltd and a bunch of other classic Pentax glass has apparently been asked to take his lunch break elsewhere, retired, kicked to the curb, pick your most salacious terms and insert here....

This rumour has no basis. No one knows anything. Some usual suspects used the retirement of Hirakawa to paint gloom and doom on Pentax. Maybe he has retired himself to enjoy life? The DA* 55/1.4, his latest creation, wasn't that great a lens anyhow, was it?

I think I'd prefer the K55/1.8 over the DA* 55/1.4. I'm happy to be proven wrong.

10-05-2010, 10:18 PM	#1
wizofoz Site Supporter Join Date: Apr 2009 Location: Melbourne, Outer east. Photos: Gallery \| Albums Posts: 1,695	Sensor size v Pentax focal lengths Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians? Is there any relationship to sensor size and square/square root factors? i.e. 31 x 1.4 = 43.4. 50 x 1.4 = 70, 55 x 1.4 = 77 Is there anything here to explain the unique Pentax focal lengths? (P.S. I'm not sure if this is correct forum, so please feel free to move it)

10-07-2010, 10:32 AM	#11
Parallax Senior Moderator Loyal Site Supporter Join Date: Apr 2008 Location: South Dakota Photos: Gallery Posts: 19,332	Your math is correct, but image circle and focal length are not the same thing. If they were lenses shorter than 28.4mm would not work. The 16-45 for example, would have one serious vignette problem at 16mm! To the OP: It has been a long held theory by some that a lens with a FL equal to the film (sensor) diagonal produces an image that looks most like what the eye sees. This was the apparent philosophy behind the FA43mm. Last edited by Parallax; 10-07-2010 at 10:43 AM.

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10-06-2010, 12:14 AM	#2
Mikheil88 Forum Member Join Date: Sep 2010 Location: Tbilisi Posts: 97	As long as I know sensor size (physical size) affects image quality. e.g. full frame sized 12MP sensor would produce better image than aps-c size 12MP sensor. But I know nothing about focal lenght affections.

10-06-2010, 12:25 AM	#3
wlachan Veteran Member Join Date: Sep 2006 Location: Canada Photos: Albums Posts: 2,625	Originally posted by wizofoz Tell me I'm crazy Okay you are crazy.

10-06-2010, 12:59 AM	#4
wizofoz Site Supporter Join Date: Apr 2009 Location: Melbourne, Outer east. Photos: Gallery \| Albums Posts: 1,695 Original Poster	Originally posted by wlachan Okay you are crazy. Thanks, I needed affirmation!

10-06-2010, 01:35 AM	#5
WerTicus Veteran Member Join Date: Mar 2009 Location: Perth Australia Photos: Albums Posts: 1,514	probably done to help you choose lotto numbers.

10-06-2010, 01:42 AM	#6
Hypocorism Veteran Member Join Date: Sep 2010 Location: Melbourne .au Posts: 623	Originally posted by wizofoz Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians? Is there any relationship to sensor size and square/square root factors? i.e. 31 x 1.4 = 43.4. 50 x 1.4 = 70, 55 x 1.4 = 77 Is there anything here to explain the unique Pentax focal lengths? Well, Britain has now formally recognised Druids as a religion, so that might have something to do with it. But seriously, yes of course you could derive many mathematical equations from the extensive range of lens focal lengths and other mfgr specs of camera components, but don't forget to account for the mythical anticlockwise vortex of draining water in the southern hemisphere and that the sun only ever rises on days that end in y. Then apply Fermet's theorem to the result and see what you get. I predict it should be mind numbing. But as we all secretly know, the underlying problem is that Pentax designers all must smoke funny weed which accounts for why only Pentax ends up producing such weirdo non-conformist focal length sizes like 31mm, 43mm, 77mm etc. with equally weirdo f/stops like 1,9, 2.4, 3.2 ad infinitum. (the mere thought of rounded numbers for simplified market understanding and sanity completely escapes them for some reason) And I also suspect that they plan a fixed 666mm zoom lens for the future, just to show Canikon who really rules the game - but don't quote me on that. Fwiw: The fear of the number 666 is known as hexakosioihexekontahexaphobia. (in case you might want to know that bit of trivia. Hope that answered your question, or at least confused you as much as you've confused everyone else with the enigma of your original post.

10-06-2010, 02:09 AM	#7
dlacouture Veteran Member Join Date: Jul 2008 Location: Var, South of France Photos: Albums Posts: 1,074	Well, 43mm is the only focal length that actually makes sense, as it's the true normal length of 24x36 (it's the diagonal of a 24x36 rectangle).

10-06-2010, 02:12 AM	#8
Spongefingers Senior Member Join Date: Aug 2008 Location: UK Photos: Gallery Posts: 237	Originally posted by wizofoz Tell me I'm crazy, but as the sensor hypotenuse of FF, crop and 4/3 sensors are roughly 30mm, 43mm and 70mm, don't the 43mm, 30mm (or 31) and 70mm measurement seem very familiar to Pentaxians? I don't think your numbers are quite in order. Don't you mean it like this: FF 135 36x24 diagonal = 43.3 APS-C (Px/Nk/So) 23.6x15.7 diagonal = 28.4 APS-C (Canon) 22.2x14.8 diagonal = 26.7 4/3rds 17.3x13 diagonal = 21.6 645 (1.3x crop) 44x33 diagonal = 55 645 (FF) 56x41.5 diagonal = 69.7 120 (square) 56x56 diagonal = 79.2 These numbers are indeed quite telling. Supposedly, a 43mm lens will have the same field of view on a 135 frame as a 70mm would have on a 645 frame, but it's never precisely the same. Originally posted by Hypocorism But as we all secretly know, the underlying problem is that Pentax designers all must smoke funny weed which accounts for why only Pentax ends up producing such weirdo non-conformist focal length sizes like 31mm, 43mm, 77mm etc. with equally weirdo f/stops like 1,9, 2.4, 3.2 ad infinitum. (the mere thought of rounded numbers for simplified market understanding and sanity completely escapes them for some reason). I figured it was because they may be more honest about the optical formulas than other companies. Also, it could be considered as an extra dimension of individuality in such desirable designs.

10-06-2010, 05:07 AM	#9
wizofoz Site Supporter Join Date: Apr 2009 Location: Melbourne, Outer east. Photos: Gallery \| Albums Posts: 1,695 Original Poster	yeah ok, so I'm looking for meaning where there is none. Obviously a slow day in the office... Oh and Hypocorism, thank you for your most elucidating reply. I cackled all the way through. ...and I like being enigmatic (and sometimes totally off the beam) Thanks for the corrections spongefingers, I had rounded the numbers, and gotr one totally out of whack. Thinks I need me some more of that funny weed.

10-07-2010, 10:02 AM	#10
RioRico Veteran Member Join Date: Jun 2008 Location: Limbo, California Posts: 11,263	There's a simple explanation for the progression: the square root of two, ~1.4. A 135/FF frame has ~twice the area of an APS-C or 135/HF frame, which has ~twice the area of an m4/3 frame; just as an f/1.4 iris opening has twice the area of an f/2 opening, which has twice the area of an f/2.8 opening, etc. Those frame diagonals are actually the diameters of the image circles needed to cover those frames. To double a circle's area, multiply the diagonal \| diameter by the square root of two, ~1.4. No magic, no coincidence, just geometry. A more telling progression is that of common focal lengths. Here is a table of that progression, and the ratios: 012mm 0.00 (like my Vemar 12) 016mm 1.33 (like my Zenitar 16) 021mm 1.31 (like my Tokina 21) 028mm 1.33 (like any 28) 037mm 1.32 (like my Mir-1) 050mm 1.35 (like any 50) 065mm 1.30 (there's a hole here) 085mm 1.31 (like a portrait 85) 105mm 1.24 (like a macro 105) 135mm 1.29 (like any 135) 180mm 1.33 (like my Meyer 180) 240mm 1.33 (like my Enna 240) If we go from 55 to 70mm, the ratio is... 1.27, close to the above ratios. Each common focal length is roughly 1/3 longer than the previous shorter FL. This suggests that changing the FL by ~1.3 gives a different enough AoV \| FoV to serve a different purpose.

10-07-2010, 08:14 PM	#12
RioRico Veteran Member Join Date: Jun 2008 Location: Limbo, California Posts: 11,263	Originally posted by Parallax Your math is correct, but image circle and focal length are not the same thing. I never said they were, just that doubled frames and doubled apertures follow the same geometrical rules re: the square root of two. [/quibble]

10-09-2010, 01:23 PM	#13
Class A Pentaxian Join Date: Aug 2008 Location: Wellington, New Zealand Posts: 11,251	Originally posted by wizofoz Is there anything here to explain the unique Pentax focal lengths? Yes, as other's explained 43mm was chosen because it results in a real normal lens. The common 50mm is a bit too long for 35mm film with a 43.3mm diagonal. BTW, this is not based on a "theory". It is a physical fact that an image viewed at the distance of the image diagonal (commonly regarded as the natural viewing distance) will show a scene with natural angles if the image was taken with the focal length of the sensor/film diagonal. Regard the 77, the designer Hirakawa wrote that they knew that a good focal length for portraiture had to be between 70mm and 80mm and that they finally went for 77mm because "77" is a lucky number in Japan. I don't know any story about the 31.

10-09-2010, 09:36 PM	#14
brecklundin Veteran Member Join Date: Jun 2009 Photos: Albums Posts: 1,674	fyi rumor has it, the dude, Hirakawa, who designed the 43ltd, 77ltd and a bunch of other classic Pentax glass has apparently been asked to take his lunch break elsewhere, retired, kicked to the curb, pick your most salacious terms and insert here.... Maybe he will go work for Canon since his cohort in that period of lense design is apparently now with Nikon...so they could compete head to head so to speak. Or the guy is gonna take his cash and enjoy life at just 48yrs old...lucky bastage!! Nothing but golf and Hello Kitty Porn... Personally I think the pink K-r lenses and bodies broke the guy...I mean a person has to have limits, right? And the thought of a camera with Notre Dame of, almost as bad, 'Frisco Junts (San Francisco Giants for those w/o a sense of humor) colors on a camera make me wanna buy a sledge hammer and a blow torch!!

10-10-2010, 01:23 PM	#15
Class A Pentaxian Join Date: Aug 2008 Location: Wellington, New Zealand Posts: 11,251	Originally posted by brecklundin fyi rumor has it, the dude, Hirakawa, who designed the 43ltd, 77ltd and a bunch of other classic Pentax glass has apparently been asked to take his lunch break elsewhere, retired, kicked to the curb, pick your most salacious terms and insert here.... This rumour has no basis. No one knows anything. Some usual suspects used the retirement of Hirakawa to paint gloom and doom on Pentax. Maybe he has retired himself to enjoy life? The DA* 55/1.4, his latest creation, wasn't that great a lens anyhow, was it? I think I'd prefer the K55/1.8 over the DA* 55/1.4. I'm happy to be proven wrong.