f value and shutter speed : what is the relation as a mathematical expression?

Discussion in 'Digital Photography' started by n, Nov 17, 2003.

  1. n

    n Guest

    I would like to understand how much faster my shutter speed could be
    letting in the same amount of light with a faster lens.

    For example, for a particular shot I used an f 2.8 lens and a shutter
    speed of 1/50.

    If I had had a different lens with an f value of 1.2 how long would
    the shutter have needed to stay open to get the same light?

    Am I right in guessing that an f 1.4 lens would need to stay open half
    as long as an f 2.8?

    What sort of lens would have an f1.0 value? Or an f0.5 value?

    I look forward to your comments.
    n, Nov 17, 2003
    #1
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  2. n

    jam Guest

    You'll find the concepts and math you need at

    www.cliffshade.com/dpfwiw/exposure.htm

    You're basically asking about reciprocity, but don't confuse the
    f-number of a lens with the f-number of a given exposure. The former
    describes the minimum f-number (maximum opening) the lens can achieve.
    (Greater openings require larger lenses and higher costs for reasons
    explained at the link above.)
    --
    Jeremy McCreary
    Denver, CO
    www.cliffshade.com/dpfwiw/
    -------------------------------------------

    "n" <> wrote in message
    news:...
    | I would like to understand how much faster my shutter speed could be
    | letting in the same amount of light with a faster lens.
    |
    | For example, for a particular shot I used an f 2.8 lens and a
    shutter
    | speed of 1/50.
    |
    | If I had had a different lens with an f value of 1.2 how long would
    | the shutter have needed to stay open to get the same light?
    |
    | Am I right in guessing that an f 1.4 lens would need to stay open
    half
    | as long as an f 2.8?
    |
    | What sort of lens would have an f1.0 value? Or an f0.5 value?
    |
    | I look forward to your comments.
    jam, Nov 17, 2003
    #2
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  3. n

    Tom Thackrey Guest

    On 17-Nov-2003, (n) wrote:

    > I would like to understand how much faster my shutter speed could be
    > letting in the same amount of light with a faster lens.
    >
    > For example, for a particular shot I used an f 2.8 lens and a shutter
    > speed of 1/50.
    >
    > If I had had a different lens with an f value of 1.2 how long would
    > the shutter have needed to stay open to get the same light?
    >
    > Am I right in guessing that an f 1.4 lens would need to stay open half
    > as long as an f 2.8?
    >
    > What sort of lens would have an f1.0 value? Or an f0.5 value?
    >
    > I look forward to your comments.


    The f/stops represent a doubling of the amount of light for each full stop,
    the stops are 1.0,1.4,2.0,2.8,4.0,5.6,8.0 ...
    If your exposure is correct at 1/50sec and f/2.8, then going to f1.4 would
    be doubling the exposure twice so, you would have to increase the shutter
    speed to 1/200th (4x) to get the same total exposure.

    f number is the ratio of the focal length of the lens to the size of the
    aperture opening. That's why it's hard to get large apertures on long
    lenses. So, an f/0.5 lens would have an opening twice it's focal length. A
    50mm lens would have a 100mm aperture opening.

    http://www.wildthingsphoto.com/tips/tip9807.htm

    --
    Tom Thackrey
    www.creative-light.com
    tom (at) creative (dash) light (dot) com
    do NOT send email to (it's reserved for spammers)
    Tom Thackrey, Nov 17, 2003
    #3
  4. n

    MarkH Guest

    (n) wrote in
    news::

    > Am I right in guessing that an f 1.4 lens would need to stay open half
    > as long as an f 2.8?


    Quarter! The f number is a ratio of diameter of aperture to the length of
    the lens, double the aperture gives 4x the light. Light gathering is
    related to the area of the opening whereas the f number is the width of the
    opening.

    When you look at the f-stop numbers, the square of those numbers show why
    each one lets in half as much light (not exact, there is some rounding):
    f-stop Square of f-stop
    1 1
    1.4 2
    2 4
    2.8 8
    4 16
    5.6 32
    8 64
    11 128
    16 256
    22 512

    I found that when I was trying to understand the f numbers the squaring of
    those numbers helped me to make sense of it.


    --
    Mark Heyes (New Zealand)
    See my pics at http://homepages.ihug.co.nz/~markh/
    "There are 10 types of people, those that
    understand binary and those that don't"
    MarkH, Nov 17, 2003
    #4
  5. n

    Alan Browne Guest

    Re: f value and shutter speed : what is the relation as a mathematicalexpression?

    n wrote:

    > I would like to understand how much faster my shutter speed could be
    > letting in the same amount of light with a faster lens.
    >
    > For example, for a particular shot I used an f 2.8 lens and a shutter
    > speed of 1/50.
    >
    > If I had had a different lens with an f value of 1.2 how long would
    > the shutter have needed to stay open to get the same light?


    Look up reciprocity. Basically a stop on the lens is a doubling or
    halving of light. A 'stop' of speed is a doubling or halving of time.
    a 'stop' of sensitivity is a doubling or halving of ISO number.

    So, for a given exposure (let's assume it is correct), a 2 stop change
    in aperture that allows more light needs to be compensated reciprically
    in speed or sensitivity or both by a total of 2 stops.

    > Am I right in guessing that an f 1.4 lens would need to stay open half
    > as long as an f 2.8?


    f/2.8 to f/1.4 is two stops. So 1/4 the time on the shutter.

    Full stops (rounded) are: f/1 f/1.4 f/2 f/2.8 f/4 f/5.6
    f/8 f11 f/16 f/22 f/32 ...

    >
    > What sort of lens would have an f1.0 value? Or an f0.5 value?


    There used to be a Canon f/1.0, but it has been discontinued, presumably
    for very low benefit/price. The theoretical limit is (I believe) f/0.7
    and at that the lens rear element would be in contact with the film/CCD
    so no room for the mirror or shutter. The shutter would need to be in
    the lens or in front of it.

    Alan

    --
    e-meil: there's no such thing as a FreeLunch.
    Alan Browne, Nov 17, 2003
    #5
  6. n

    Alan Browne Guest

    Re: f value and shutter speed : what is the relation as a mathematicalexpression? -COR

    Correction below ((CORR)).

    Alan Browne wrote:

    >
    >
    > n wrote:
    >
    >> I would like to understand how much faster my shutter speed could be
    >> letting in the same amount of light with a faster lens.
    >>
    >> For example, for a particular shot I used an f 2.8 lens and a shutter
    >> speed of 1/50.
    >>
    >> If I had had a different lens with an f value of 1.2 how long would
    >> the shutter have needed to stay open to get the same light?

    >
    >
    > Look up reciprocity. Basically a stop on the lens is a doubling or
    > halving of light. A 'stop' of speed is a doubling or halving of time. a
    > 'stop' of sensitivity is a doubling or halving of ISO number.
    >
    > So, for a given exposure (let's assume it is correct), a 2 stop change
    > in aperture that allows more light needs to be compensated reciprically
    > in speed or sensitivity or both by a total of 2 stops.
    >
    >> Am I right in guessing that an f 1.4 lens would need to stay open half
    >> as long as an f 2.8?

    >
    >
    > f/2.8 to f/1.4 is two stops. So 1/4 the time on the shutter.
    >
    > Full stops (rounded) are: f/1 f/1.4 f/2 f/2.8 f/4 f/5.6
    > f/8 f11 f/16 f/22 f/32 ...
    >
    >>
    >> What sort of lens would have an f1.0 value? Or an f0.5 value?

    >
    >
    > There used to be a ((CORR)) Canon f/1.2 ((CORR)), but it has been discontinued, presumably
    > for very low benefit/price. The theoretical limit is (I believe) f/0.7
    > and at that the lens rear element would be in contact with the film/CCD
    > so no room for the mirror or shutter. The shutter would need to be in
    > the lens or in front of it.
    >
    > Alan
    >


    --
    e-meil: there's no such thing as a FreeLunch.
    Alan Browne, Nov 17, 2003
    #6
  7. n

    Flux Guest

    Re: f value and shutter speed : what is the relation as a mathematicalexpression?

    MarkH wrote:

    > (n) wrote in
    > news::
    >
    >
    >>Am I right in guessing that an f 1.4 lens would need to stay open half
    >>as long as an f 2.8?

    >
    >
    > Quarter! The f number is a ratio of diameter of aperture to the length of
    > the lens, double the aperture gives 4x the light. Light gathering is
    > related to the area of the opening whereas the f number is the width of the
    > opening.
    >
    > When you look at the f-stop numbers, the square of those numbers show why
    > each one lets in half as much light (not exact, there is some rounding):
    > f-stop Square of f-stop
    > 1 1
    > 1.4 2
    > 2 4
    > 2.8 8
    > 4 16
    > 5.6 32
    > 8 64
    > 11 128
    > 16 256
    > 22 512
    >
    > I found that when I was trying to understand the f numbers the squaring of
    > those numbers helped me to make sense of it.


    It follows from this that each stop number is equal to the previous stop
    multiplied by the square root of 2. This means that if you are at an
    arbitrary aperture number (say, 4.5), to get double the exposure you'd have
    to open up to 4.5/SQRT(2) = 3.2 (rounded).

    This happens because the light intensity is directly proportional to the
    area of the opening, and that is proportional to the diameter squared (and
    the f number is the ratio between the focal length and the diameter).


    Flux
    Flux, Nov 17, 2003
    #7
  8. n

    Argon3 Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    I seem to remember that Stanley Kubrick used lenses faster than f1.0 to film
    "Barry Lindon". The scenes were lit by candlelight...at the time it was quite
    a technical achievement.

    argon
    Argon3, Nov 17, 2003
    #8
  9. n

    Ken' Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    I don't think there is such a thing.
    Leica have a 50 MM F 1.0 but it is the only one as far as I know.
    Ken'


    "Argon3" <> wrote in message
    news:...
    > I seem to remember that Stanley Kubrick used lenses faster than f1.0 to

    film
    > "Barry Lindon". The scenes were lit by candlelight...at the time it was

    quite
    > a technical achievement.
    >
    > argon
    Ken', Nov 17, 2003
    #9
  10. Re: f value and shutter speed : what is the relation as a mathematical

    (Argon3) writes:

    > I seem to remember that Stanley Kubrick used lenses faster than f1.0 to
    > film "Barry Lindon". The scenes were lit by candlelight...at the time it
    > was quite a technical achievement.


    "Fortunately, I found just such a lens, one of a group of ten which Zeiss
    had specially manufactured for NASA satellite photography. The lens had a
    speed of fO.7, and it was 100% faster than the fastest movie lens."
    http://www.visual-memory.co.uk/amk/doc/interview.bl.html

    I recall an interview where he made a different statement about the source
    of his cameras, but I can't find it. My recollection is that the cameras
    were in existence at a studio, and he conned them out of them in some way.

    --
    Philip Stripling | email to the replyto address is presumed
    Legal Assistance on the Web | spam and read later. email to philip@
    http://www.PhilipStripling.com/ | my domain is read daily.
    Phil Stripling, Nov 17, 2003
    #10
  11. Re: f value and shutter speed : what is the relation as a mathematical

    [top-posting fixed]

    "Ken'" <> writes:

    > "Argon3" <> wrote in message news:...


    > > I seem to remember that Stanley Kubrick used lenses faster than
    > > f1.0 to film "Barry Lindon". The scenes were lit by
    > > candlelight...at the time it was quite a technical achievement.


    > I don't think there is such a thing.


    You'd be wrong about that. They're fairly rare, and don't play
    heavily in the consumer market for obvious reasons.

    Closest I can quickly find online to a citation is an archived message
    from a guy claiming he saw details on it in a Kubrick biography show:
    <http://lists.cdegroot.com/pipermail/yashicacontax-slr/2001-November/000638.html>

    But I also remember reading about it at the time.

    > Leica have a 50 MM F 1.0 but it is the only one as far as I know.


    Canon EF 50mm F1.0 also existed.

    Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    it at Photokina one year LONG ago. I believe it was something like
    40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    (It was their response to people complaining about how slow their
    lenses were; essentially saying "it's easy to make fast lenses if you
    don't care about image quality".)
    --
    David Dyer-Bennet, <>, <www.dd-b.net/dd-b/>
    RKBA: <noguns-nomoney.com> <www.dd-b.net/carry/>
    Photos: <dd-b.lighthunters.net> Snapshots: <www.dd-b.net/dd-b/SnapshotAlbum/>
    Dragaera/Steven Brust: <dragaera.info/>
    David Dyer-Bennet, Nov 18, 2003
    #11
  12. n

    eric ng Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    Lens with f1.0 does exist but I had not a chance to use them because they
    are rare. I've used a Cannon 55mm f1.2,
    fantastic lens made by the Japanese!

    "David Dyer-Bennet" <> wrote in message
    news:-b.net...
    > [top-posting fixed]
    >
    > "Ken'" <> writes:
    >
    > > "Argon3" <> wrote in message

    news:...
    >
    > > > I seem to remember that Stanley Kubrick used lenses faster than
    > > > f1.0 to film "Barry Lindon". The scenes were lit by
    > > > candlelight...at the time it was quite a technical achievement.

    >
    > > I don't think there is such a thing.

    >
    > You'd be wrong about that. They're fairly rare, and don't play
    > heavily in the consumer market for obvious reasons.
    >
    > Closest I can quickly find online to a citation is an archived message
    > from a guy claiming he saw details on it in a Kubrick biography show:
    >

    <http://lists.cdegroot.com/pipermail/yashicacontax-slr/2001-November/000638.
    html>
    >
    > But I also remember reading about it at the time.
    >
    > > Leica have a 50 MM F 1.0 but it is the only one as far as I know.

    >
    > Canon EF 50mm F1.0 also existed.
    >
    > Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    > it at Photokina one year LONG ago. I believe it was something like
    > 40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    > (It was their response to people complaining about how slow their
    > lenses were; essentially saying "it's easy to make fast lenses if you
    > don't care about image quality".)
    > --
    > David Dyer-Bennet, <>, <www.dd-b.net/dd-b/>
    > RKBA: <noguns-nomoney.com> <www.dd-b.net/carry/>
    > Photos: <dd-b.lighthunters.net> Snapshots:

    <www.dd-b.net/dd-b/SnapshotAlbum/>
    > Dragaera/Steven Brust: <dragaera.info/>
    eric ng, Nov 18, 2003
    #12
  13. n

    jean Guest

    jean, Nov 18, 2003
    #13
  14. n

    jpc Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    On 17 Nov 2003 21:10:09 -0600, David Dyer-Bennet <>
    wrote:



    >Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    >it at Photokina one year LONG ago. I believe it was something like
    >40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    >(It was their response to people complaining about how slow their
    >lenses were; essentially saying "it's easy to make fast lenses if you
    >don't care about image quality".)



    Isn't an f# of 0.5 the theoredical limit. As I remember an F 0.5 lens
    has a field of view of 180 degrees. Any faster lens would require that
    light coming from behind the lens be imaged on or near the focal plane
    which IMHO doesn't sound possible.
    jpc, Nov 18, 2003
    #14
  15. Re: f value and shutter speed : what is the relation as a mathematical

    "eric ng" <> writes:

    > Lens with f1.0 does exist but I had not a chance to use them because they
    > are rare. I've used a Cannon 55mm f1.2,
    > fantastic lens made by the Japanese!


    Rare *and expensive*. Fastest I've got is the Nikon 58mm f1.2 NOCT
    (no official f1.0 or faster lenses available for Nikon; not that I
    could afford them if they were).
    --
    David Dyer-Bennet, <>, <www.dd-b.net/dd-b/>
    RKBA: <noguns-nomoney.com> <www.dd-b.net/carry/>
    Photos: <dd-b.lighthunters.net> Snapshots: <www.dd-b.net/dd-b/SnapshotAlbum/>
    Dragaera/Steven Brust: <dragaera.info/>
    David Dyer-Bennet, Nov 18, 2003
    #15
  16. Re: f value and shutter speed : what is the relation as a mathematical

    jpc <> writes:

    > On 17 Nov 2003 21:10:09 -0600, David Dyer-Bennet <>
    > wrote:
    >
    >
    >
    > >Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    > >it at Photokina one year LONG ago. I believe it was something like
    > >40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    > >(It was their response to people complaining about how slow their
    > >lenses were; essentially saying "it's easy to make fast lenses if you
    > >don't care about image quality".)

    >
    > Isn't an f# of 0.5 the theoredical limit. As I remember an F 0.5 lens
    > has a field of view of 180 degrees. Any faster lens would require that
    > light coming from behind the lens be imaged on or near the focal plane
    > which IMHO doesn't sound possible.


    No theoretical limit that I can see. No correlation between field of
    view and f number, either. Remember, the F number is simply the ratio
    of the lens focal length to the lens diameter. It's perfectly
    possible to make a lens of 50mm focal length (say) that's huge (say
    1000mm in diameter). Such a lens would be f 50/1000, that is, f .05.
    --
    David Dyer-Bennet, <>, <www.dd-b.net/dd-b/>
    RKBA: <noguns-nomoney.com> <www.dd-b.net/carry/>
    Photos: <dd-b.lighthunters.net> Snapshots: <www.dd-b.net/dd-b/SnapshotAlbum/>
    Dragaera/Steven Brust: <dragaera.info/>
    David Dyer-Bennet, Nov 18, 2003
    #16
  17. n

    fruitbat Guest

    Re: f value and shutter speed : what is the relation as a mathematical expression? -COR

    On 11/17/2003, Alan Browne wrote:
    >
    > There used to be a ((CORR)) Canon f/1.2 ((CORR)), but it has been
    > discontinued, presumably for very low benefit/price. The
    > theoretical limit is (I believe) f/0.7 and at that the lens rear
    > element would be in contact with the film/CCD so no room for the
    > mirror or shutter. The shutter would need to be in the lens or in
    > front of it.


    You were right the first time. There was an EF 50/1.0. While Canon has
    taken the link to it off of their EF lens pages, you can still find it
    here:

    http://www.usa.canon.com/eflenses/lenses/ef_50_1/ef_50_1.html

    Jeff
    fruitbat, Nov 18, 2003
    #17
  18. n

    Don Stauffer Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    I have even seen an f0.95 by one of the major camera mfgs, I think it
    was Nikon. During a short stint as a lens designer I designed an f0.7
    lens, but it was for laser light, and hence monochromatic, and spherical
    aberration was not an important concern. Image quality was of course
    very poor, but it was for a missile tracker, and so image quality wasn't
    important.

    eric ng wrote:
    >
    > Lens with f1.0 does exist but I had not a chance to use them because they
    > are rare. I've used a Cannon 55mm f1.2,
    > fantastic lens made by the Japanese!
    >
    > "David Dyer-Bennet" <> wrote in message
    > news:-b.net...
    > > [top-posting fixed]
    > >
    > > "Ken'" <> writes:
    > >
    > > > "Argon3" <> wrote in message

    > news:...
    > >
    > > > > I seem to remember that Stanley Kubrick used lenses faster than
    > > > > f1.0 to film "Barry Lindon". The scenes were lit by
    > > > > candlelight...at the time it was quite a technical achievement.

    > >
    > > > I don't think there is such a thing.

    > >
    > > You'd be wrong about that. They're fairly rare, and don't play
    > > heavily in the consumer market for obvious reasons.
    > >
    > > Closest I can quickly find online to a citation is an archived message
    > > from a guy claiming he saw details on it in a Kubrick biography show:
    > >

    > <http://lists.cdegroot.com/pipermail/yashicacontax-slr/2001-November/000638.
    > html>
    > >
    > > But I also remember reading about it at the time.
    > >
    > > > Leica have a 50 MM F 1.0 but it is the only one as far as I know.

    > >
    > > Canon EF 50mm F1.0 also existed.
    > >
    > > Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    > > it at Photokina one year LONG ago. I believe it was something like
    > > 40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    > > (It was their response to people complaining about how slow their
    > > lenses were; essentially saying "it's easy to make fast lenses if you
    > > don't care about image quality".)
    > > --
    > > David Dyer-Bennet, <>, <www.dd-b.net/dd-b/>
    > > RKBA: <noguns-nomoney.com> <www.dd-b.net/carry/>
    > > Photos: <dd-b.lighthunters.net> Snapshots:

    > <www.dd-b.net/dd-b/SnapshotAlbum/>
    > > Dragaera/Steven Brust: <dragaera.info/>


    --
    Don Stauffer in Minnesota

    webpage- http://www.usfamily.net/web/stauffer
    Don Stauffer, Nov 19, 2003
    #18
  19. n

    Don Stauffer Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    We must not confuse normal definition of FOV with the f/number
    acceptance cone angle. Yes, 0.5 is limit for normal lens, whereas it is
    possible with lower f/number lenses to have FOVs exceeding 180. These
    later type lenses have a relatively high f/number and REALLY extreme
    distortion, but it CAN be done. The lenses produce a toroidal format.

    jpc wrote:
    >
    > On 17 Nov 2003 21:10:09 -0600, David Dyer-Bennet <>
    > wrote:
    >
    > >Then there was the Zeiss Super-Q Gigantar. Really. Well, they showed
    > >it at Photokina one year LONG ago. I believe it was something like
    > >40mm f0.33. Consisted of a couple of enlarger condensors in a mount.
    > >(It was their response to people complaining about how slow their
    > >lenses were; essentially saying "it's easy to make fast lenses if you
    > >don't care about image quality".)

    >
    > Isn't an f# of 0.5 the theoredical limit. As I remember an F 0.5 lens
    > has a field of view of 180 degrees. Any faster lens would require that
    > light coming from behind the lens be imaged on or near the focal plane
    > which IMHO doesn't sound possible.


    --
    Don Stauffer in Minnesota

    webpage- http://www.usfamily.net/web/stauffer
    Don Stauffer, Nov 19, 2003
    #19
  20. n

    MikeWhy Guest

    Re: f value and shutter speed : what is the relation as a mathematical

    "Don Stauffer" <> wrote in message
    news:...
    > I have even seen an f0.95 by one of the major camera mfgs, I think it
    > was Nikon. During a short stint as a lens designer I designed an f0.7
    > lens, but it was for laser light, and hence monochromatic, and spherical
    > aberration was not an important concern. Image quality was of course
    > very poor, but it was for a missile tracker, and so image quality wasn't
    > important.


    Great. A color blind, myopic warhead. :)
    "it was for a missile tracker, and so and so image quality wasn't
    important."
    MikeWhy, Nov 20, 2003
    #20
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