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calculating focal length required

Discussion in 'General Technical Discussion' started by clickcanada, Jul 17, 2008.

  1. I was just wondering if there was a formula that is used to figure the focal length that would be needed for a given situation?:confused: 

    For example, what focal length would be needed for shooting sports when you are 100 feet away? Or bird shooting from 100 feet away? It would be helpfull to know some simple way to calculate a basic starting point for a given situation.

    Thanks all.
  2. gvk


    Jun 17, 2005
    Mystic, CT
    Algebraic rearrangement of the Gaussian lens equation gives the result,

    s = (1 + 1/m) f

    where s is the distance to the subject, f is the focal length, and m the magnification. Thus

    f = s / (1 + 1/m)

    Magnification is the image size over the subject size. For a 6 foot athlete in portrait orientation you need a field at least 2 m high. Assuming a DX camera,

    1/m = 2 / 0.024 = 83 (where both subject and sensor height are in meters)

    For a subject 100 ft away, or about 30 m

    f = 30 / (1 + 83) = 0.357 m

    You will need a 300 mm lens and either crop a bit or try to get a little closer. You can do a similar calculation if you know what size birds you want to shoot and either solve for the required focal length, or the subject distance for the known focal length of one of your lenses.
  3. LDB415


    Apr 26, 2008
    Is there a version of that available in English? :confused: 
  4. gvk


    Jun 17, 2005
    Mystic, CT
    Image size is approximately proportional to focal length for subject distances much longer than the focal length.
  5. ok, I had to go through it a few times, but I have it now.

    Thanks Gerry
  6. I would say "it depends on how you want to compose."

    Do you want only a single player? Or do you want the whole scrum? A player flying through the air and those around him, or a sportrait?

  7. You mean there actually was a good reason I took algebra? :eek: :biggrin:
  8. My reason for wanting this info is more to help me figure what my next lens purchase should be. I thought I would take a more scientific approach and look at what I would like to shoot and think about how I would capture it. Then do some math and find the optimal focal range to look for.

    I currently have a sigma 10-20 and 18-50 with a Nikkor 85mm f/1.8. I have been debating over a 50-150mm or to go long and go with a 70-200 and forget that I have a small hole from 50 to 70mm. I thought that if I did a little math I could skip over the buy-and-try method.:rolleyes:  It looks like the longer range is the best way for me to go, thanks for the math lesson.:cool: 
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