With so many choices these days in wide-field eyepieces it can become confusing what with the interplay between magnification and field of view. (See Reviewing the Fundamentals below.)
For example, let's say you have your eye on one of the newer 82° or 100° apparent field of view eyepieces (or, you'd like to). But, your question is, "What size eyepiece should I get (in one line of eyepieces) to achieve a particular field of view in another line?". But, do you want to go through the trial-and-error process of picking an EP then calculating it's magnification then the resulting field-of-view?
I.e., Mag (X) = FLt/FLep (i)
And, from that, the true field-of-view (TFOV) is equal to the apparent field of view (AFOV) of an eyepiece divided by the system's magnification, from above ...
So, TFOV = AFOV (ii)
Substituting for MAG in (i) above ...
TFOV = AFOV (iii)
Or, stated another way ...
TFOV = AFOV x FLep (iv)
Therefore, the focal length of the eyepiece I would need, solving for FLep, is ...
FLep = TFOV x FLt
I.e., to determine what EP focal length is needed for a desired True Field of View (TFOV), multiply by the focal length of the telescope and divide by the new EP's AFOV.
Example: Given an 8 inch f/10 SCT of focal length 2032.
You would like to have that 82°, 30mm EP, but it's expensive.
So, you're looking at a line of EPs with 72° (or, 68°).
Now, the TFOV of that would-be-nice-to-have 82°/30mm in the 8" SCT is 1.21°.
To achieve the equivalent FOV in the 72° line of EPs,
you would need .... 1.21 x 2032 / 72. Or, a ~34mm ep. (You would probably opt for the 36mm that is available.
In a 68° line of EP's, you would need a ~36mm eyepiece.
Or, in this example, 2032/25 = 81.28x.
Or, in this example, 68° / 81.28 = .8366°.
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