Lens Trivia: Figuring Half-Stops

[Mark Sawyer]

Just a little lens trivia some may not know...

Most all of us have the standard f/stops memorized: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, 90...

And most of us know that the value doubles every other stop...

But do you know how to figure what the half-stop is in-between the standard stops?

Say you have an f/6.3 Tessar, an f/6.5 Cooke Series III, an f/6.7 Fujinon W, and an f/6.8 Dagor. Which is exactly mid-point between f/5.6 and f/8?

Anybody know how to figure it? It's pretty simple!

[Kevin Crisp]

When the pointer is right between two numbers?

[Mark Sawyer]

When the pointer is right between two numbers?

Nope! We're talking an actual numerical value!

[TXFZ1]

I was going to give the same flippant answer, but it's logarithmic and thought I heard of an easy remembrance to help out. f/5.6...f6.3.^.f7.1...f/8.

David

[R.K]

https://en.wikipedia.org/wiki/F-number

It all explained there.

[photog_ed]

A quick way to figure it is to multiply the next lower F/# by 2^(1/4) = 1.189.

Ed

[Mark Sawyer]

I was going to give the same flippant answer, but it's logarithmic and thought I heard of an easy remembrance to help out. f/5.6...f6.3.^.f7.1...f/8.

David

Nope, those are third-stops, and I don't want to memorize the whole scale...



https://en.wikipedia.org/wiki/F-number

It all explained there.

They don't explain how to figure half stops, (and some of what they do explain is wrong...)


A quick way to figure it is to multiply the next lower F/# by 2^(1/4) = 1.189.

Ed

There's a quicker way...

To find a half-stop, just add the two stops that are lower than the stops on either side. So for the stop half-way between f/5.6 and f/8, just add 2.8 and 4. So f/6.8 is half-way between! Half-way between f/16 and f/22 would be 8 +11 = f/19. Etc...

[TXFZ1]

You missed the "^".:) So, now tell why I should care if it is 6.8 or 6.6596.

David

[Jac@stafford.net]

We can calculate fractional F-stops to the end of math, but neither our lenses nor shutter speeds are accurate enough to matter.
.

[Mark Sawyer]

...So, now tell why I should care if it is 6.8 or 6.6596.

David


We can calculate fractional F-stops to the end of math, but neither our lenses nor shutter speeds are accurate enough to matter.
.

That's why it's lens TRIVIA!

[Kevin Crisp]

Practical answer does not equal flippant answer.

[Paul Metcalf]

Thanks Mark. I appreciated this.

[photog_ed]

Nope, those are third-stops, and I don't want to memorize the whole scale...




They don't explain how to figure half stops, (and some of what they do explain is wrong...)



There's a quicker way...

To find a half-stop, just add the two stops that are lower than the stops on either side. So for the stop half-way between f/5.6 and f/8, just add 2.8 and 4. So f/6.8 is half-way between! Half-way between f/16 and f/22 would be 8 +11 = f/19. Etc...

OK, this bothered me all day, so I worked it out. This is an approximate method that depends on the approximation 2*sqrt(2) ~ 3. So if 2.828... is close enough to 3 for you then you are good to go.

Ed

[Struan Gray]

Actually, you are solving the quartic equation

x^4 + x^2 - x = 0

There are four roots. two of them are complex. None of them are the forth root of two.

[AA+]

I prefer to just write out the sequence
Best wishes --- Allen

1/2 stops calculate by factor 2^(1/4)
1/3 stops calculate by factor 2^(1/6)

1/2 stops: f/1 f/1.2 f/1.4 f/1.7 f/2 f/2.4 f/2.8 f/3.4 f/4
1/3 stops: f/1 f/1.12 f/1.26 f/1.4 f/1.6 f/1.8 f/2 f/2.2 f/2.5 f/2.8 f/3.2 f/3.6 f/4

1/2 stops: f/4 f/4.7 f/5.6 f/6.7 f/8 f/9.5 f/11 f/13 f/16
1/3 stops: f/4 f/4.5 f/5 f/5.6 f/6.3 f/7 f/8 f/9 f/10 f/11 f/13 f/14 f/16

1/2 stops: f/16 f/19 f/22.6! f/27 f/32 f/38 f/45 f/54 f/64
1/3 stops: f/16 f/18 f/20 f/22.6! f/25 f/28 f/32 f/36 f/40 f/45 f/51 f/57 f/64

1/2 stops: f/64 f/76 f/90 f/108 f/128
1/3 stops: f/64 f/72 f/81 f/90 f/102 f/114 f/128

[Jac@stafford.net]

This has been an academically interesting discussion, but our LF lenses are so likely to have inaccurate shutter speeds that FAPP I would ignore 1/2 F-stop nuances.
.

[Doremus Scudder]

This has been an academically interesting discussion, but our LF lenses are so likely to have inaccurate shutter speeds that FAPP I would ignore 1/2 F-stop nuances.
.

I doesn't hurt to try and be a little more accurate. I have a shutter-speed tester that I use to find the actual speeds on all my shutters and then label the lensboard with speeds to the closest 1/3 stop. I then use intermediate aperture settings, also in 1/3-stop increments to get my exposures as close as I can (while being aware that there is an inherent margin of error in the system).

FWIW, a whole stop underexposure with transparency materials will yield an unusable slide... even a half-stop is pushing it. Striving for accuracy in exposure is the only way to get even close. Ignoring a half-stop "nuance" that is compounded by other errors in the system can result in severe exposure problems.

One-third-stop increments are how my meter reads, how film speeds are indicated and how filter factors and graphs of curves, etc. are marked. I see no reason to use half-stop increments instead, although it's interesting to know.

Best,

Doremus

[TXFZ1]

Same here, except I've not tested my shutter speeds. My meter is set in thirds and most of my lenses are marked in thirds. I just do not sit down and calculate or try to remember the approximation for the actual f/stop number. I'm happy with keeping that in the black box.

David

[DrTang]

hell.. as sloppy as I am with my development times... a third stop here or there taint pis

[Jeff Keller]

Square root of the square root of 2 = square root of 1.4142 = 1.1892

either divide or multiply to go down or up. It is proportional to the area of the lens which increases with the square of the radius.