Given the rather huge price differences between eye pieces at the same focal length. How exactly does the AFOV affect the view seen through the eyepiece?
Are higher / lower AFOV better for certain situations? or is higher always better?
[Physics] Optimal Angular Field of View (AFOV)
astronomyopticstelescopes
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John, your method for determining approximate lens focal lengths is a valid one, although since your eye will automatically accommodate to some extent, accuracy will be limited.
The apparent discrepancies follow from the rather obscure convention of labeling lens "Power" in units of Diopters, which are inverse meters.
The power P of an optic is defined as the inverse of the focal length f in meters:
$$ P = \frac{1}{f} $$
Thus a lens of power $-3$ has a focal length of $-1/3$ meter or $-33$ $cm$, not far from the $f= -30$ $cm$ you estimated. Similarly, a power of $-0.25$ Diopters corresponds to $-4$ $m$ or $-400$ $cm$, a very weak negative lens which would scarcely be noticeable when combined with a fairly high powered positive lens (magnifier).
If the object is in the focal plane of the lens then the upright, virtual image is seen at infinity - parallel rays of light enter the eye.
Bringing the object closer to the lens also brings the virtual image closer and the angular magnification also increases.
With the unaided eye the3 greatest magnification is obtained when the virtual image is as close as it can be whilst the optical surfaces within the eye still produce a focussed image on the retina.
That distance is called the least distance of distinct vision and usually is taken to be 25 cm.
So the position of the virtual image as seen by the eye varies as the position of the object varies.
You might find using the Phet Geometrical Optics simulation informative?
Here are some screen shots:
Best Answer
Simply, a larger FOV provides a wider hunk of sky in the eyepiece. This is useful for capturing entire objects at higher magnifications than could be obtained with cheaper eye-pieces. It doesn't provide more light, just a wider view. As for better, if you've gone to the expense of buying one for a given focal length, it'll still work just as well as something cheaper so may as well use it.