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F-Ratio for Eyepiece Projection Photography

If you use a 35mm camera with eyepiece projection, for bright objects the camera’s meter will give you exposure information but you need to know the effective f-ratio for the entire optical system (i.e. the “lens” f-stop) to pick the shutter speed.  The effective f-ratio depends on the scope’s focal length, the eyepiece focal length, and the distance between the eyepiece and the film plane in the camera. Since the distance between the eyepiece and the film plane in the camera varies depending on how you have set up the system, you need to compute the effective f-ratio for your setup. Here are the formulas: Do this all in the same units, which means millimeters since that’s the number you know for your eyepiece.

First calculate the Magnification (M) of the system:

      M = (S - F2)/F2      where:

       S = distance from the eyepiece to the film plane
       F2 = the focal length of the eyepiece

      You can use a metric ruler to get the approximate the distance, in millimeters, from the eyepiece to the film plane.  The film plane is usually shown on the top of SLR cameras, by a circle with a line running through it.

Then F, the effective focal length of the system, is

      F = F1 x M     where:

      F1 = focal length of the telescope (i.e. 2030mm for an 8” f/10 SCT)
      M = Magnification (from the first formula above)

Finally, f, the effective focal ratio of the system, is

      f = F/D          where

      D = the diameter of the scope’s primary mirror or lens (203mm for an 8” scope)

For example, suppose you are using a 15mm eyepiece that is 30mm from the film plane. The magnification M would be (30 - 15)/15 or 2.0 - you are magnifying the image by a factor of 2.  The effective focal length F would be 2000x2 = 4000mm. The effective focal ratio would be 4000/203 = 20.  This means that this setup with a 15” eyepiece has turned the f/10 scope into an f/20 scope - not surprising considering that magnifying an image (which is what you’re doing with eyepiece projection) reduces the delivered light a lot.

Don’t worry too much about getting the distance “S” exact. In this type of photography you want to bracket exposures anyway, and the above calculation will get you into the ballpark.

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