Size lens to get for medium to long range recording.

Discussion in 'Beginner Questions' started by limbskars94, Dec 8, 2020.

  1. You're right as the formula is applicable only to a right triangle so you have to split the angle in half as 2 right triangles.
     
  2. It's always best to do something the right way, which works every time.

    Yes, focal lengths as written on lenses etc. are nominal. That's no reason to introduce yet another source of error by also using incorrect maths.
     
  3. And yet my rough 'n' ready calculation came up with 17.3ft (correct), while for some reason James' method arrived at 17.49ft (inaccurate).
     
  4. What formula?
    The half-angle method is only applicable if you've already been given the angle-of-view of the lens*.
    If you only know the sensor size and focal length, then you have to work out the tangent for yourself.

    Say we have a 20mm lens on a 24mm wide sensor. Dividing 24 by 20 to get a tangent gives exactly the same result as dividing 12 (the half sensor-width) by 20 and then multiplying by 2.

    So why walk all around the block to get back where you started?

    * The published angles-of-view for lenses are usually the useless diagonal angle. And how often do you tip the camera diagonally to get all of a subject in frame?
     
  5. For the sake of completeness, here's a diagram showing why working with half-angles is a waste of time, if all you want to know is the subject width/height covered.
    Subject-size.png
    X is the unknown subject dimension
    D is the subject distance
    S is the sensor width or height
    F is the lens effective focal length

    You can see by the theory of similar triangles that X will be the same in both cases, but it's much easier to cut to the chase and use the simpler formula on the right.

    Incidentally, the right hand diagram is the same as for a shifted lens.

    NB. The angles involved aren't the same in both cases, but that's irrelevant if all we need to know is the subject height or width.
     

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