The correct way to think about focal length

**rparmar** · 05-09-2023, 07:17 AM - **1 Like**

Here's the correct way to think about focal length. Let the debate begin.

Apologies to my Pentax friends that I am using Lumix S lenses as the data. But exactly the same thinking applies to any system. Though the actual numbers here apply only to so-called full-frame (135).

And, hey, I am using Pentax glass on the Lumix, so there's that.

Wheatfield · 05-09-2023, 07:58 AM - **4 Likes**

The first sentence says everything one needs to know about the article.

James O'Neill · 05-09-2023, 08:35 AM

Quote field of view instead of how much the lens bends light ? It has some attractions.
But consider. I have a 77 mm lens on my K1. The diagonal of the sensor is Square-root(36*36 +24*24) = 43.26mm. It's view angle is 2arcTan ( (43.26 / 2) / 77 ) = 31.4 degrees.
When I crop from 7360x4912 pixels to say 5000x4000 I'm using a piece of the sensor 25x20 and now I need to say it's a 23 degree angle of view. If I put the K1 into "square frame" mode the image view angle is 25 degrees, if I put the lens on the K5 its a 21 degree lens. I don't even want to guess what it is adapted to, saym micro four thirds. The angle doesn't change by the same factor as the sensor size. However if change the focal length by the same factor as the image size we do get the same angle.
Easier to say, I used this focal length, on this sensor size and resolution and I've cropped that to the resolution you see.

Because of the legacy of 35mm film we DO convert the combination of focal length / sensor size into its 35mm equivalent, and that isn't perfect
The 77 on a crop sensor camera has the angle of view of a 115mm on a 35mm one, but at f/8 it has less effective DOF that it would have on FF (because the picture is enlarged more) but more than 115mm has at the same aperture on 35mm. Well we could replace f/ numbers so they were not indications of focal length divided by aperture diameter, and all 21.2 degree lenses had aperture positions giving the same d.o.f. regardless of their actual focal length But then when we went to set the exposure at a given aperture we'd run into trouble.

The only thing a lens maker knows for sure is the focal length of the glass, the size of the hole in the light goes through and how big the image will be when it's formed.

jgnfld · 05-09-2023, 08:36 AM

Can't say I'm impressed with the stats or the coding. It is incredibly elementary. The chart itself might be nice enough to examine..

James O'Neill · 05-09-2023, 09:01 AM

By the way, I've been down the rat-hole with this

The Field of View (FoV) AKA angle of view tells you how wide your vista will be. And that's important not only for what fits into the frame, but for how objects are rendered in relationship to distance. (That's a different article.)

Field of view does not OF ITSELF change how objects are rendered with distance. There's a very simple though experiment for this. Set up a tripod with a k1 and lens, take a picture. Now put the camera in crop mode. what the lens puts on the active part of the sensor hasn't changed because the rest of the sensor isn't being used.
If things are 1 meter apart and we shoot 2M from the nearest one, 1M from the nearest one and 0.5M from the nearest one THAT changes the perspective effect - the far object is 1.5x times the distance, double the distance and 3x the distance. If we fit a lens with twice the focal length the near object might be too big, so we move twice as far away, so instead of being 2+1, 1+1, 0.5+1 the distances are 4+1, 2+1, and 1+1, so the far object is 1.25x 1.5x and 2x the distance. Angle of view makes us change where we stand to take the shot, and changing position changes how objects are rendered with distance.

**UncleVanya** · 05-09-2023, 09:36 AM

This article at least tries to clarify why 16mm vs 20mm is a larger difference than 500 vs 510 for example.

What is missing is the perspective that wildlife shooting versatility is more than simply a range of angle of views.

Wheatfield · 05-09-2023, 11:09 AM

Originally posted by UncleVanya

This article at least tries to clarify why 16mm vs 20mm is a larger difference than 500 vs 510 for example..

Anyone with a primary school education in mathematics should be able to figure that one out.

jgnfld · 05-09-2023, 12:45 PM

Originally posted by Wheatfield

Anyone with a primary school education in mathematics should be able to figure that one out.

Well middle school more likely.

jcdoss · 05-09-2023, 12:52 PM - **2 Likes**

Originally posted by Wheatfield

The first sentence says everything one needs to know about the article.

Thanks for saving me a bunch of time. 👍

pschlute · 05-09-2023, 02:58 PM - **1 Like**

Oh Lordy. If anyone needs to read an article like this to understand what FL is, they had a very poor start in their photographic learning to begin with.

**UncleVanya** · 05-09-2023, 05:24 PM

Originally posted by Wheatfield

Anyone with a primary school education in mathematics should be able to figure that one out.

The logical fallacy is that math could be used to say 4 is less than 10, but a more agile mind may argue that we need to compare % of focal length change. If we do the difference between 20mm and 40mm should be proportionally the same as between 200mm and 400mm.

Using this logic is a 20mm vs. a 40mm the same as a 200mm vs. a 400mm? Let's agree the ratio is the same. 1/2 or 2x depending on the direction of the comparison. Looking at the angle of view the tale is a little more crooked...

Diagonal Angle of view (FF):
20mm = 94 degrees
40mm = 57 degrees
94/57=1.64

200mm = 12 degrees
400mm = 6.2 degrees
12/6.2 = 1.93

Clearly by this metric the 200/400 ratio is higher and proves well... not much. LOL. Lens focal lengths are often expressed in even numbers because that's what marketing people do. Pentax was weird and gave us the 43 and 31 and 77 - who else does that??? We aren't dealing with perfect numbers and the angle of view may be more accurate than the focal length.

In any case I think it is a useful way to point people to the right idea who might be new to photography but it isn't revolutionary by any means. Anyone with much time behind a lens knows that the focal length differences at the short end can be astounding while they are less easily noticed at the long end unless you are shooting very small objects like birds. And even then - the percentage of focal length not the absolute focal length is what starts to compete with angle of view as a metric.

Lord Lucan · 05-10-2023, 02:24 AM

Originally posted by jgnfld

Can't say I'm impressed with the stats or the coding. It is incredibly elementary.

I was not impressed that the web site designer used links to Flickr in order to show their own images - why not put the image in the code directly? I gave up when I was faced with the Flickr cookie questionaire.

Originally posted by UncleVanya

Lens focal lengths are often expressed in even numbers because that's what marketing people do. Pentax was weird and gave us the 43 and 31 and 77 - who else does that???

Odd numbers? Other than multiples of 5 like 35, 85 and 135 I suppose. 43mm was once popular as a fixed lens FL because it is the diagonal of a 35mm frame, and such a lens was claimed therefore to give a natural perspective. My first 35mm camera (one of my father's cast-offs) had a 43 mm lens.

**UncleVanya** · 05-10-2023, 05:12 AM

Originally posted by Lord Lucan

I was not impressed that the web site designer used links to Flickr in order to show their own images - why not put the image in the code directly? I gave up when I was faced with the Flickr cookie questionaire.

Odd numbers? Other than multiples of 5 like 35, 85 and 135 I suppose. 43mm was once popular as a fixed lens FL because it is the diagonal of a 35mm frame, and such a lens was claimed therefore to give a natural perspective. My first 35mm camera (one of my father's cast-offs) had a 43 mm lens.

Other than Pentax I’ve not seen a 43mm claimed focal length. Many 40mm lenses likely aren’t exactly 40 is my point.

Wheatfield · 05-10-2023, 07:18 AM

Originally posted by UncleVanya

Other than Pentax I’ve not seen a 43mm claimed focal length. Many 40mm lenses likely aren’t exactly 40 is my point.

My very first camera was a Fujica rangefinder that had a 4.5cm lens. Not 43mm, but close enough in this case, and it may well have been a bit shorter anyway. I've occasionally thought it odd that even though I learned on that focal length and got some very good pictures with that camera I have never had much use for my 43LTD.
The other day I went back and pulled some of those 50+ year old negs and their corresponding prints and it turns out everything I did with that camera was cropped a bit when I printed the negs. Apparently even back then I didn't really like the wide standard, preferring something somewhat longer.

jgnfld · 05-10-2023, 09:24 AM

My 40mm SMC Ltd is almost a go-to for me when it is golden hour. Renders things beautifully.

05-09-2023, 07:17 AM - 1 Like	#1
rparmar Site Supporter Join Date: Jan 2008 Photos: Gallery Posts: 8,819	The correct way to think about focal length Here's the correct way to think about focal length. Let the debate begin. Apologies to my Pentax friends that I am using Lumix S lenses as the data. But exactly the same thinking applies to any system. Though the actual numbers here apply only to so-called full-frame (135). And, hey, I am using Pentax glass on the Lumix, so there's that.

05-10-2023, 02:24 AM	#12
Lord Lucan Pentaxian Join Date: Sep 2017 Location: South Wales Photos: Gallery Posts: 2,963	Originally posted by jgnfld Can't say I'm impressed with the stats or the coding. It is incredibly elementary. I was not impressed that the web site designer used links to Flickr in order to show their own images - why not put the image in the code directly? I gave up when I was faced with the Flickr cookie questionaire. Originally posted by UncleVanya Lens focal lengths are often expressed in even numbers because that's what marketing people do. Pentax was weird and gave us the 43 and 31 and 77 - who else does that??? Odd numbers? Other than multiples of 5 like 35, 85 and 135 I suppose. 43mm was once popular as a fixed lens FL because it is the diagonal of a 35mm frame, and such a lens was claimed therefore to give a natural perspective. My first 35mm camera (one of my father's cast-offs) had a 43 mm lens. Last edited by Lord Lucan; 05-10-2023 at 04:43 AM.

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05-09-2023, 07:58 AM - 4 Likes	#2
Wheatfield Moderator Join Date: Apr 2008 Location: The wheatfields of Canada Posts: 15,981	The first sentence says everything one needs to know about the article.

05-09-2023, 08:35 AM	#3
James O'Neill Veteran Member Join Date: Apr 2023 Posts: 351	Quote field of view instead of how much the lens bends light ? It has some attractions. But consider. I have a 77 mm lens on my K1. The diagonal of the sensor is Square-root(3636 +2424) = 43.26mm. It's view angle is 2arcTan ( (43.26 / 2) / 77 ) = 31.4 degrees. When I crop from 7360x4912 pixels to say 5000x4000 I'm using a piece of the sensor 25x20 and now I need to say it's a 23 degree angle of view. If I put the K1 into "square frame" mode the image view angle is 25 degrees, if I put the lens on the K5 its a 21 degree lens. I don't even want to guess what it is adapted to, saym micro four thirds. The angle doesn't change by the same factor as the sensor size. However if change the focal length by the same factor as the image size we do get the same angle. Easier to say, I used this focal length, on this sensor size and resolution and I've cropped that to the resolution you see. Because of the legacy of 35mm film we DO convert the combination of focal length / sensor size into its 35mm equivalent, and that isn't perfect The 77 on a crop sensor camera has the angle of view of a 115mm on a 35mm one, but at f/8 it has less effective DOF that it would have on FF (because the picture is enlarged more) but more than 115mm has at the same aperture on 35mm. Well we could replace f/ numbers so they were not indications of focal length divided by aperture diameter, and all 21.2 degree lenses had aperture positions giving the same d.o.f. regardless of their actual focal length But then when we went to set the exposure at a given aperture we'd run into trouble. The only thing a lens maker knows for sure is the focal length of the glass, the size of the hole in the light goes through and how big the image will be when it's formed.

05-09-2023, 08:36 AM	#4
jgnfld Moderator Loyal Site Supporter Join Date: Feb 2015 Location: Avalon Peninsula, Newfoundland Photos: Gallery \| Albums Posts: 1,789	Can't say I'm impressed with the stats or the coding. It is incredibly elementary. The chart itself might be nice enough to examine..

05-09-2023, 09:01 AM	#5
James O'Neill Veteran Member Join Date: Apr 2023 Posts: 351	By the way, I've been down the rat-hole with this The Field of View (FoV) AKA angle of view tells you how wide your vista will be. And that's important not only for what fits into the frame, but for how objects are rendered in relationship to distance. (That's a different article.) Field of view does not OF ITSELF change how objects are rendered with distance. There's a very simple though experiment for this. Set up a tripod with a k1 and lens, take a picture. Now put the camera in crop mode. what the lens puts on the active part of the sensor hasn't changed because the rest of the sensor isn't being used. If things are 1 meter apart and we shoot 2M from the nearest one, 1M from the nearest one and 0.5M from the nearest one THAT changes the perspective effect - the far object is 1.5x times the distance, double the distance and 3x the distance. If we fit a lens with twice the focal length the near object might be too big, so we move twice as far away, so instead of being 2+1, 1+1, 0.5+1 the distances are 4+1, 2+1, and 1+1, so the far object is 1.25x 1.5x and 2x the distance. Angle of view makes us change where we stand to take the shot, and changing position changes how objects are rendered with distance.

05-09-2023, 09:36 AM	#6
UncleVanya Loyal Site Supporter Join Date: Jul 2014 Photos: Gallery \| Albums Posts: 28,404	This article at least tries to clarify why 16mm vs 20mm is a larger difference than 500 vs 510 for example. What is missing is the perspective that wildlife shooting versatility is more than simply a range of angle of views.

05-09-2023, 11:09 AM	#7
Wheatfield Moderator Join Date: Apr 2008 Location: The wheatfields of Canada Posts: 15,981	Originally posted by UncleVanya This article at least tries to clarify why 16mm vs 20mm is a larger difference than 500 vs 510 for example.. Anyone with a primary school education in mathematics should be able to figure that one out.

05-09-2023, 12:45 PM	#8
jgnfld Moderator Loyal Site Supporter Join Date: Feb 2015 Location: Avalon Peninsula, Newfoundland Photos: Gallery \| Albums Posts: 1,789	Originally posted by Wheatfield Anyone with a primary school education in mathematics should be able to figure that one out. Well middle school more likely.

05-09-2023, 12:52 PM - 2 Likes	#9
jcdoss Pentaxian Join Date: Nov 2012 Location: Ingelheim am Rhein, Germany Photos: Gallery \| Albums Posts: 6,769	Originally posted by Wheatfield The first sentence says everything one needs to know about the article. Thanks for saving me a bunch of time. 👍

05-09-2023, 02:58 PM - 1 Like	#10
pschlute Moderator Loyal Site Supporter Join Date: Mar 2007 Location: Surrey, UK Photos: Gallery Posts: 8,202	Oh Lordy. If anyone needs to read an article like this to understand what FL is, they had a very poor start in their photographic learning to begin with.

05-09-2023, 05:24 PM	#11
UncleVanya Loyal Site Supporter Join Date: Jul 2014 Photos: Gallery \| Albums Posts: 28,404	Originally posted by Wheatfield Anyone with a primary school education in mathematics should be able to figure that one out. The logical fallacy is that math could be used to say 4 is less than 10, but a more agile mind may argue that we need to compare % of focal length change. If we do the difference between 20mm and 40mm should be proportionally the same as between 200mm and 400mm. Using this logic is a 20mm vs. a 40mm the same as a 200mm vs. a 400mm? Let's agree the ratio is the same. 1/2 or 2x depending on the direction of the comparison. Looking at the angle of view the tale is a little more crooked... Diagonal Angle of view (FF): 20mm = 94 degrees 40mm = 57 degrees 94/57=1.64 200mm = 12 degrees 400mm = 6.2 degrees 12/6.2 = 1.93 Clearly by this metric the 200/400 ratio is higher and proves well... not much. LOL. Lens focal lengths are often expressed in even numbers because that's what marketing people do. Pentax was weird and gave us the 43 and 31 and 77 - who else does that??? We aren't dealing with perfect numbers and the angle of view may be more accurate than the focal length. In any case I think it is a useful way to point people to the right idea who might be new to photography but it isn't revolutionary by any means. Anyone with much time behind a lens knows that the focal length differences at the short end can be astounding while they are less easily noticed at the long end unless you are shooting very small objects like birds. And even then - the percentage of focal length not the absolute focal length is what starts to compete with angle of view as a metric.

05-10-2023, 05:12 AM	#13
UncleVanya Loyal Site Supporter Join Date: Jul 2014 Photos: Gallery \| Albums Posts: 28,404	Originally posted by Lord Lucan I was not impressed that the web site designer used links to Flickr in order to show their own images - why not put the image in the code directly? I gave up when I was faced with the Flickr cookie questionaire. Odd numbers? Other than multiples of 5 like 35, 85 and 135 I suppose. 43mm was once popular as a fixed lens FL because it is the diagonal of a 35mm frame, and such a lens was claimed therefore to give a natural perspective. My first 35mm camera (one of my father's cast-offs) had a 43 mm lens. Other than Pentax I’ve not seen a 43mm claimed focal length. Many 40mm lenses likely aren’t exactly 40 is my point.

05-10-2023, 07:18 AM	#14
Wheatfield Moderator Join Date: Apr 2008 Location: The wheatfields of Canada Posts: 15,981	Originally posted by UncleVanya Other than Pentax I’ve not seen a 43mm claimed focal length. Many 40mm lenses likely aren’t exactly 40 is my point. My very first camera was a Fujica rangefinder that had a 4.5cm lens. Not 43mm, but close enough in this case, and it may well have been a bit shorter anyway. I've occasionally thought it odd that even though I learned on that focal length and got some very good pictures with that camera I have never had much use for my 43LTD. The other day I went back and pulled some of those 50+ year old negs and their corresponding prints and it turns out everything I did with that camera was cropped a bit when I printed the negs. Apparently even back then I didn't really like the wide standard, preferring something somewhat longer.

05-10-2023, 09:24 AM	#15
jgnfld Moderator Loyal Site Supporter Join Date: Feb 2015 Location: Avalon Peninsula, Newfoundland Photos: Gallery \| Albums Posts: 1,789	My 40mm SMC Ltd is almost a go-to for me when it is golden hour. Renders things beautifully.