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Thread started 09 Apr 2009 (Thursday) 17:44

# Lenses in stops

Apr 09, 2009 17:44 |  #1
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We usually measure f-ratios (the quotient of the focal length and aperture) in stops, with f/1 meaning the diameter of the apparent aperture equals the effective focal length.

So, I was thinking that it would be interesting to consider the focal lengths of lenses in stops as well. For f/1, we would choose where the effective focal length of the lens equals the length of the sensor diagonal.

To that end, let me present some common focal lengths in mm and in stops, using a 35mm FF sensor:

12mm ~ -1.85 stops
14mm ~ -1.63 stops
15mm ~ -1.53 stops
16mm ~ -1.44 stops
17mm ~ -1.35 stops

24mm ~ -0.85 stops
28mm ~ -0.63 stops

35mm ~ -0.31 stops
50mm ~ 0.21 stops

70mm ~ 0.69 stops
85mm ~ 0.97 stops

100mm ~ 1.21 stops
135mm ~ 1.65 stops
150mm ~ 1.79 stops
180mm ~ 2.06 stops
200mm ~ 2.21 stops
300mm ~ 2.79 stops

400mm ~ 3.21 stops
500mm ~ 3.53 stops
600mm ~ 3.79 stops
800mm ~ 4.21 stops

The reason for the breaks is how we classify lenses:

Below -1 stops: UWA (ultra wide angle)
Between -1 and -0.5 stops: WA (wide angle)
Between -0.5 and 0.5 stops: normal
Between 0.5 stops and 1 stop: short telephoto
Between 1 and 3 stops: telephoto
Longer than 3 stops: super telephoto

And, yes, for those that are wondering, I do. : )

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Apr 09, 2009 17:47 |  #2

Hmm, you are indeed good at math. What is the usefulness of this though?

Gear

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Apr 09, 2009 18:03 |  #3
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jklewer wrote in post #7700229
Hmm, you are indeed good at math. What is the usefulness of this though?

No "usefulness" at all, that I can think of at the moment. Just interesting. Same as with my photography, save the "interesting" part. : )

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Apr 09, 2009 18:08 |  #4

joe mama wrote in post #7700300
No "usefulness" at all, that I can think of at the moment. Just interesting. Same as with my photography, save the "interesting" part. : )

HAHA, a mathematician with a sense of humor to boot..!

Gear

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Apr 09, 2009 18:23 |  #5

3.14159265358979323

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EF 24-105mm f/4L IS USM, EF 70-200mm f/4L IS USM,
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Apr 09, 2009 18:25 |  #6

Ugh........

Math makes me cringe....... *shiver*

1D Mark II_40D w/grip_16-35 L f/2.8_24-70 L f/2.8_70-200 L f/2.8_100-400 L f/4.5-

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Apr 09, 2009 18:43 |  #7
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jklewer wrote:
HAHA, a mathematician with a sense of humor to boot..!

When you look like me, your choices are limited... : )

CameraLens wrote:
3.14159265358979323

A little late to the party, no? I think they're to 4 billion digits now. : )

TheSportsGuy wrote:
---------------

Ugh........

Math makes me cringe....... *shiver*

As it does a lot of people, which is a shame. I mean, for sure you can get through life fine without it, and this thread is good evidence of that, but math is, quite literally, a language. And while it's a poor choice of languages for many things, such as love, play, and sex (wait -- did I just say the same thing three times in a row?), it's a beautiful language that let's you talk about and understand a lot of other things.

Granted, those other things may hold no appeal to you (and most), but I think it's cool to understand the things that math can talk about. I mean, going through life without understanding math is like going through life without being able to sing and dance. You can do it just fine, and most people don't feel they miss a thing, but I do. Especially 'cause I can't sing or dance. : )

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Apr 09, 2009 18:54 |  #8

joe mama wrote in post #7700509
As it does a lot of people, which is a shame. I mean, for sure you can get through life fine without it, and this thread is good evidence of that, but math is, quite literally, a language. And while it's a poor choice of languages for many things, such as love, play, and sex (wait -- did I just say the same thing three times in a row?), it's a beautiful language that let's you talk about and understand a lot of other things.

Granted, those other things may hold no appeal to you (and most), but I think it's cool to understand the things that math can talk about. I mean, going through life without understanding math is like going through life without being able to sing and dance. You can do it just fine, and most people don't feel they miss a thing, but I do. Especially 'cause I can't sing or dance. : )

I hear ya for sure. I took many calculus classes a few years ago in school, struggled through all of them. I changed my major than realized how much more I understood because I had a good math knowledge. CHAMPION the math my friend, keep spreading the word!

Gear

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Apr 09, 2009 19:01 |  #9

CameraLens wrote in post #7700395
3.14159265358979323

Ever seen questions on the M-CAT (test for admission to medical school)?

for the test, pi can be assumed to be 3.

and acceleration due to gravity is assumed to be 10 m/sec^2 (instead of 9.81 or 32.2 feet/sec^2 like we used in engineering classes)

2009 Red River Flooding- Grand Forks, North Dakota
https://photography-on-the.net …3177&posted=1#p​ost7613177
Canon Rebel XSi, 18-55mm IS, 55-250mm IS II, 50mm f/1.8 II
Canonet QL-17 G-III Rangefinder (40mm fixed, f/1.7-f/16) with no batteries needed!

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Apr 09, 2009 19:01 |  #10

I'm too damn old to learn another/different system.

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Apr 09, 2009 19:18 as a reply to  @ joe mama's post |  #11

As it does a lot of people, which is a shame. I mean, for sure you can get through life fine without it, and this thread is good evidence of that, but math is, quite literally, a language. And while it's a poor choice of languages for many things, such as love, play, and sex (wait -- did I just say the same thing three times in a row?), it's a beautiful language that let's you talk about and understand a lot of other things.

Granted, those other things may hold no appeal to you (and most), but I think it's cool to understand the things that math can talk about. I mean, going through life without understanding math is like going through life without being able to sing and dance. You can do it just fine, and most people don't feel they miss a thing, but I do. Especially 'cause I can't sing or dance. : )[/QUOTE]

That is understandable.... I am terrible, and when I mean terrible, I mean TERRIBLE at math..lol

I'm an art person, I can play instruments, draw, photograph, design, etc, but I can't do math. I guess that my reasoning side that controls math and language functions is very much lacking compared to the creative side of my brain....lol

1D Mark II_40D w/grip_16-35 L f/2.8_24-70 L f/2.8_70-200 L f/2.8_100-400 L f/4.5-

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Apr 09, 2009 19:22 |  #12

I think it is more useful to use magnifcation factor, both linear and area, especially as ranges of prime lenses were designed with these magnifications in mind, in the past. I reckon that is more useful because that gives an indication of how much the enlargement is, and how much of the area of a standard lens you see. The standard should actually be 50 mm, because that is what we are used to.

The word stops in this context is actually very confusing, as this indicates a link to light involved in exposure, which in your calculation doesn't compute .

Also, classification of lenses into categories is time dependent. F.e., in the past, 20-25 years ago or so, we considered 24 mm as UWA, 28 and 35 mm WA, and anything rectlinear beyond an AoV of 90 degrees as extreme UWA. I think nowadays these definitions have shifted a little down.

Anyway, let me make a little table too, FL, magnification factor relative to 50 mm, linear view factor relative to 50 mm (how much more or less you see in a linear fashion compared to 50mm), area magnification factor and area of view factor relative to 50 mm (which part of the frame or how much more of a frame you see compared to the field of view of a 50 mm) .

12mm - 0.24 - 4.17 - 0.058 - 17.36
14mm - 0.28 - 3.57 - 0.078 - 12.76
15mm - 0.30 - 3.33 - 0.090 - 11.11

16mm - 0.32 - 3.13 - 0.010 - 9.77
17mm - 0.34 - 2.94 - 0.012 - 8.65
18mm - 0.36 - 2.78 - 0.130 - 7.72
19mm - 0.38 - 2.63 - 0.144 - 6.93
20mm - 0.40 - 2.50 - 0.160 - 6.25
21mm - 0.42 - 2.38 - 0.176 - 5.67

24mm - 0.48 - 2.08 - 0.23 - 4.34
25mm - 0.50 - 2.00 - 0.25 - 4.00
28mm - 0.56 - 1.79 - 0.31 - 3.19

35mm - 0.70 - 1.43 - 0.49 - 2.04
40mm - 0.80 - 1.25 - 0.64 - 1.56
45mm - 0.90 - 1.11 - 0.81 - 1.23
50mm - 1.00 - 1.00 - 1.00 - 1.00
55mm - 1.10 - 0.91 - 1.21 - 0.83
58mm - 1.16 - 0.86 - 1.35 - 0.74
60mm - 1.20 - 0.83 - 1.44 - 0.69

70mm - 1.4 - 0.71 - 1.96 - 0.51
80mm - 1.6 - 0.63 - 2.56 - 0.39
85mm - 1.7 - 0.59 - 2.89 - 0.34
90mm - 1.8 - 0.56 - 3.24 - 0.31

100mm - 2.0 - 0.50 - 4.0 - 0.250
105mm - 2.1 - 0.48 - 4.4 - 0.227
120mm - 2.4 - 0.42 - 5.8 - 0.174
125mm - 2.5 - 0.40 - 6.3 - 0.160
135mm - 2.7 - 0.37 - 7.3 - 0.137
150mm - 3.0 - 0.33 - 9.0 - 0.111
180mm - 3.6 - 0.28 - 13.0 - 0.077
200mm - 4.0 - 0.25 - 16.0 - 0.063

240mm - 4.8 - 0.208 - 23 - 0.0434
280mm - 5.6 - 0.179 - 31 - 0.0319
300mm - 6.0 - 0.167 - 36 - 0.0278
350mm - 7.0 - 0.143 - 49 - 0.0204
400mm - 8.0 - 0.125 - 64 - 0.0156
450mm - 9.0 - 0.111 - 81 - 0.0123
480mm - 9.6 - 0.104 - 92 - 0.0109

500mm - 10.0 - 0.100 - 100 - 0.0100
560mm - 11.2 - 0.089 - 125 - 0.0080
600mm - 12.0 - 0.083 - 144 - 0.0069
700mm - 14.0 - 0.071 - 196 - 0.0051
800mm - 16.0 - 0.063 - 256 - 0.0039

1000mm - 20 - 0.050 - 400 - 0.0025
1100mm - 22 - 0.045 - 484 - 0.0021
1200mm - 24 - 0.042 - 576 - 0.0017

If you do feel like calculating something in f-stops, what about theoretical vignetting for the corners of the frame of a list of lenses, considering center is 0 stops? I would certainly find that useful, but am now too lazy to look up the formula .

Kind regards, Wim

EOS R & EOS 5 (analog) with a gaggle of primes & 3 zooms, OM-D E-M1 Mk II & Pen-F with 10 primes, 6 zooms, 3 Metabones adapters/speedboosters​, and an accessory plague

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Apr 09, 2009 19:35 |  #13

Holy \$h!t!

2009 Red River Flooding- Grand Forks, North Dakota
https://photography-on-the.net …3177&posted=1#p​ost7613177
Canon Rebel XSi, 18-55mm IS, 55-250mm IS II, 50mm f/1.8 II
Canonet QL-17 G-III Rangefinder (40mm fixed, f/1.7-f/16) with no batteries needed!

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Apr 09, 2009 19:38 |  #14

also can you give titles to each group of focal lenths as you have them split? UWA, WA, normal, telephoto, etc.?

2009 Red River Flooding- Grand Forks, North Dakota
https://photography-on-the.net …3177&posted=1#p​ost7613177
Canon Rebel XSi, 18-55mm IS, 55-250mm IS II, 50mm f/1.8 II
Canonet QL-17 G-III Rangefinder (40mm fixed, f/1.7-f/16) with no batteries needed!

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Apr 09, 2009 19:40 |  #15
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jklewer wrote:
I hear ya for sure. I took many calculus classes a few years ago in school, struggled through all of them. I changed my major than realized how much more I understood because I had a good math knowledge. CHAMPION the math my friend, keep spreading the word!

It is cool, sometimes, though, isn't it? I mean, to see something happen and understand why? For example, my daughter just moved to second grade. Out of 85 second grade students and 21 of them from her previous class, only 3 of the kids from that class are in her new class of 17 students. What were the chances of that? Was my daughter being separated on purpose? Well, as it turns out, there's a 43% that there would be 3 or fewer, actually. : )

Brian XTi wrote:
Ever seen questions on the M-CAT (test for admission to medical school)?

Actually, that's my day job. : )

for the test, pi can be assumed to be 3.

Even worse when the politicians get into it:

http://www.straightdop​e.com …-a-law-saying-pi-equals-3

I mean, geez, if there was ever a group of people who needed to know math, it's our "leaders".

and acceleration due to gravity is assumed to be 10 m/sec^2 (instead of 9.81 or 32.2 feet/sec^2 like we used in engineering classes)

You might be interested to know that of all the physical constants in nature, the Gravitational Constant, G, is known with the least precision:

http://en.wikipedia.or​g/wiki/Gravitational_c​onstant

due to the difficulty in accurately measuring it. So if pi, the most precisely calculated constant known, can be rounded to 3, I think we can forgive them for rounding the least precisely known of all the physical constants to the same level of precision. : )

I'm too damn old to learn another/different system.

I'm too damn old to date a young hottie. You'd be surprised what some nice clothes, a nice car, sounding smart, and a harmless lie ("I'm a doctor") will get you. If Micael Douglas wasn't too old for Katherine Zeta-Jones, then, my friend, you ain't too old to learn something useless. : )

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Lenses in stops
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