57.3

[Ags]

I have just discovered this most wonderful formula:

true field of view = (eyepiece field stop * 57.3) / telescope focal length

So, my 24mm hyperion has a field stop of 29mm and my scope has a FL of 1325mm, giving:

True FOV = (29 * 57.3) / 1325 = 1.25 degrees

This is the real field of view, independent of the curvy things an eyepiece might do to the field which prevents the simple AFOV/Mag formula from giving an accurate answer.

It leaves me wondering about two things:

1. Where does the magic number 57.3(degrees) come from?

2. Why don't EP manufacturers quote their field stop sizes, as this is so fundamental to eyepiece function?

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For my 24mm hyperion, the AFOV/Mag formula suggests my field of view is 1.23 degrees. So the true field has been compressed by about two percent (presumably in a pincushiony way).

[John]

I've come across the 57.3 figure but I don't know how it's derived - I'd be interested to know though.

Tele Vue do publish their field stop sizes and plenty of other specs on their eyepieces but some other brands are rather shy about it. We might get some surprises if we took a pair of calipers to some of them !.

With many eyepiece designs using a smyth-type lens set below the field stop it's it bit difficult to get the calipers in to find out.

There is always the method of timing a star drifting across the field of view ......

[FraserClarke]

1. Where does the magic number 57.3(degrees) come from?

It's a radian... a fundamental measure of angle in that a circle is made of 2*pi radians. Not an arbitrary division like a degree.

[Rob_Jn]

57.3 is the number of degrees in a radian or 180/Pi.

For some reason a lot of equations concerning angular measure use radians.

Rob.

[Ags]

OK, 57.3 is one radian converted to degrees. But... (I have the sense I'm being dense...) why is the value 1 radian?

In what way is a radian fundamental though? Isn't it just a mathematically convenient way of measuring angles?

[Rob_Jn]

Good question, we'll have to get someone in more mathematically competent to answer that

[FraserClarke]

In what way is a radian fundamental though? Isn't it just a mathematically convenient way of measuring angles?

No, pi is very fundamental in that it is the ratio of a circle's diameter to it's circumference. So things that work in exact fractions of pi are also geometrically fundamental, not just mathematically convenient. A radian is I think the angle of an arc for which the length of the arc is equal to the radius of the arc. So it's geometrically defined, rather than just "made up" like degrees are (which I think are just 360 because the babylonians liked numbers that were convenient to divide -- I think??).

As to why it appears the way it does in your equation, my brain is refusing to understand just now . But it will be relating a linear size (the field stop) to an angle (the field of view).

[Ags]

Why 360 degrees? Perhaps the Babylonians thought that the year 'ought' to be 360 days long, but a demon or somesuch inserted 5 unlucky days!

[toml42]

I think it's just an approximation still, the radian is just to convert it into an angle

[FraserClarke]

Yeah, the days in the year explanation seems pretty reasonable as a basis. And 360 is much more easily divisible than 365, so mathematically much more useful.

[toml42]

ah, i think i've figured it out, it looks like the small angle approximation for sin

sin(x) = L1/L2

when x ( in radians ) is small:

x = L1 / L2

to convert to degrees:

angle = L1 * 57.3 / L2

[FraserClarke]

D'oH. Yes, I think you're right Tom.

Which in fact makes this equation exactly the same as the AFOV / mag equation. As (I guess!?!);

AFOV (degrees) = 57.3 * Field Stop / Focal Length (eyepiece)

mag = Focal Length (telescope) / Focal Length (eyepiece)

FOV = AFOV / mag = (57.3 * Field Stop / Focal Length (eyepiece) ) / (Focal Length (telescope) / Focal Length (eyepiece) )

Focal Length (eyepiece) cancels out, and you get the original equation...

[Ags]

That's a new formula to me: AFOV = field stop * 57.3 / EP focal length

Obviously it's the counterpart of the formula for true FOV (you just swap the telescope and EP focal length, which intuitively sounds logical).

That seems to imply that there is an iron relationship between the AFOV and the field stop. Actually I don't think that is completely true as the eyepiece introduces aberrations like pincushion that make the real AFOV slightly different to the theoretical AFOV calculated from the field stop. Which is the point of the field stop formula for true field; it is immune to the effect of such aberrations.

[mcrossley]

I have a calculator for this on my website