For most of these formulas, you will need to know three things:
- Aperture size, in mm.
(Diameter of the objective mirror or lens)
- Focal Length, in mm.
(Distance from the lens or mirror to the point of focus)
- Eyepiece focal Length, in mm
(Distance from the lens to the point of focus - is negative!)
= (A / 7)2
A is the telescope's aperture in mm
7mm is the size of the average pupil
The primary purpose of a telescope is to gather light. As a scope's aperture
increases, it will gather more light and will be able to more faint objects.
= Fe / fs
Fe is the eyepiece's focal length in mm
fs is the scope's focal ratio
The exit pupil is the apparent size of the image in the eyepiece. Remember that
the pupil is 6 or 7 mm. An overly large or small exit pupil can be annoying.
f = F/A
f is the scope's focal ratio
F is the scope's focal length in mm
A is the scope's aperture in mm
The Focal Ratio is written as an f-number, like f/6. While this number
looks like a camera's f-number, a telescope's focal ratio is an indicator of the field of
view, not film speed. Look on the examples page for
clarification.
Dawes Limit = 116" / A
116" (arc seconds) is the constant determined by Dawes
A is scope aperture in mm
Basically, this is a measure of the smallest features visible in a scope. Dawes,
an English astronomer, originally defined the limit using a 25mm (one-inch) telescope and
two 6th magnitude stars. The magnitude of the stars is a factor - brighter stars
will cause bleed-over, darker stars won't be as visible, and uneven pairs are harder to
split. This is the theoretical limit, but "seeing" usually degrades the
"splitting" ability.
= (2 * Dawes Limit * 3476) / 1800
2*Dawes Limit is the scope's working resolution
3476 is the moon's diameter in kilometers
1800 is moon's angular size in arc seconds
The result is in kilometers and is a measure of the smallest lunar features visible in
a scope. You will be able to see objects as small as ?? kilometers.
= a / M
or
= a / (Fs / Fe)
a is the eyepiece's apparent field of view (AFOV)
M is the eyepiece's magnification on this scope
Fs is the scope's focal length in mm
Fe is the eyepiece's focal length in mm
AFOV is the angular diameter (in degrees) that the eye sees through a lens. A
scope's design determines the possible FOV range and the combination of the eyepiece and
scope create a unique FOV within that range.
Eyepieces are negative lenses - They actually expand the light, unlike magnifying
(objective) lenses which focus light to a point,. When you combine a telescope's
objective lens or mirror with an eyepiece lens, you get a magnified view with a small (7
degrees or less) field of view.
Each eyepiece design has a field of view built into it. Older eyepieces have
narrow FOVs (30-40 degrees), modern eyepieces commonly have 40 or 50 degree FOV, while
advanced eyepieces like Naglers can have an FOV of 80 degrees. Narrow FOV eyepieces
suffer from a narrow view and can be disappointing. Wide FOV eyepieces can suffer
from shadows and distortions. Normal FOVs present a good blend of
undistorted view and FOV.
M = Fs / Fe
Fs is the scope's focal length in mm
Fe is the eyepiece's focal length in mm
Magnification is useful in observing, but is not the prime purpose of a telescope.
Very high magnification can often be useless, especially in smaller scopes.
Views of 600x are sure to disappoint because the view will be very narrow,
very dark, very prone to shaking, and hard to keep the subject in
view. See the examples page for the
magnifications I regularly use on my scopes.
= A / 7
A is the telescope aperture in mm
7mm is the dilated eye
This formula produces the lowest magnification that produces a 7mm exit pupil.
There is much dissention on this subject. Does a field of view larger than the pupil
diameter waste light or simply provide a view to "swim around"? Perhaps
it's more a personal choice than a scientific decision.
= A / 0.63
A is the telescope aperture in mm
0.63mm is the minimum diameter the average eye can contract
This limit is based on the smallest your pupils can contract. The theoretical
maximum is 1.58 * mm of aperture, but working values are often double
this value.
In both cases, useful magnification is often limited by seeing, dirt and dust on the
optics, and the inherent brightness of the object in view. The
physiology of the eye also plays a part - It's made of many packed
detector cells and excessive magnification turns the picture into a grainy
view as the detail gets expanded beyond this limit. For a good analogy, magnify a newspaper photo - you'll
see a conglomeration of dots that make little sense, yet are a recognizable picture at
lower magnification.
