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Image Size

The linear size, S, of an object at the focal plane of a system will depend on the object's angular size, theta, and the focal length of the system, F, according to:

            theta  *  F



      S = ---------------



                q











      where q = 57.3 if q is in degrees,



              = 3438 if q is in minutes of arc,



              = 206264 if q is in seconds of arc

The units of S will be the same as the units of F.

For small diameter objects such as planets or lunar features, long effective focal lengths are required to produce a reasonable image size. The normal focal length of a telescope, Fo, can be increased by projection. Three common projection methods are used.

Afocal Projection

In the afocal projection system, the telescope and eyepiece are focused on an abject and the camera, with its lens in place and focused at infinity, is placed behind the eyepiece. Given the camera lens focal length, Fc, and telescope/eyepiece magnification, M, the system focal length is:

      F = M x Fc

For best image formation, it is necessary that the eyepiece exit pupil have the same location as the camera entrance pupil. This is often impossible due to the mechanical design of the eyepiece and the camera.

Positive or Eyepiece Projection

If a positive lens or eyepiece of focal length Fp is used to project the image a distance d, then magnification and resulting system focal length are found by:

            d



      M = -------  - 1          magnification



            Fp







      F = M x Fo

Negative or Barlow Projection

If a negative lens such as a barlow lens of (negative) focal length Fn is used to project the image a distance d, then the magnification and resulting system focal length are found by:

            d



      M = ------- + 1          magnification



            Fp







      F = M x Fo

Angular Size of Some Solar System Objects

• Moon: 32.7' (perigee) to 28.5' (apogee)
• Sun: 32.6' (perihelion) to 31.5' (aphelion)
• Mercury: 5" (superior conjunction) to 13" (inferior conjunction)
• Venus: 10" (superior conjunction) to 64" (inferior conjunction)
• Mars: 4" (conjunction) to 25" (opposition)
• Jupiter: 31" (conjunction) to 48" (opposition)
• Saturn:
  -- disc: 15" (conjunction) to 21" (opposition)
  -- rings: 34" (conjunction) to 45" (opposition)
• Uranus: 3" (conjunction) to 4" (opposition)
• Neptune: 2.5"

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