CFAS Beginner's Class
Telescope Formulas
Last updated 01-06-2014
Aperture = diameter of the main optic
Focal Length = distance from the main optic to the focal plane
Focal Length
Focal Ratio = -----------------Aperture
Telescope Focal Length
Aperture
Magnification = --------------------------------- = --------------Eyepiece Focal Length
Exit Pupil
Eyepiece Focal Length
Aperture
Exit Pupil = -------------------------------- = ------------------Focal Ratio
Magnification
Eyepiece field stop diameter
Apparent FOV
True Field Of View (FOV) = ---------------------------------------- * 57.3  --------------------Telescope Focal Length
Magnification
For example, let's consider a 6 inch telescope with a focal length of 48 inches.
The Focal Ratio = 48 ÷ 6 = 8, so this is a 6" f/8 telescope.
Now, let's put a 25 mm eyepiece with a 50 degree apparent field of view into the telescope.
To compute the magnification, we need to convert the focal lengths for the telescope and the
eyepiece into like units. Since most eyepieces have their focal lengths specified in millimeters (mm),
let's convert the telescope focal length from inches to millimeters. 1 inch = 25.4 mm, so this telescope
is 48 inches x 25.4 = 1,219.2 mm, so...
The Magnification = 1219.2 ÷ 25 = 46.768.
The Exit Pupil = 25 ÷ 8 = 3.125 mm.
The True FOV = 50 ÷ 46.768 = 1.07 degrees.
The first method of determining the true FOV yields radians, so to convert this to degrees, we multiply
by 57.3. Also, the first method of determining the True FOV is precisely accurate, but most eyepiece
manufacturers don't specify the field stop diameters of their eyepieces, so the second method of
dividing the Apparent FOV by the Magnification is most commonly used. This second method is an
approximation, but it is generally fairly close to the real number.