The focal length of a mirror determines the FOV (Field Of View) for a given area at the primary focus. The formula for it is given below. The FOV as calculated by this formula is the circular diameter of the part of the sky that will be projected on the given area.
This formula is best explained with an example. Suppose you want a FOV of 1 degree to have a circle with a radius of 5 mm around the optical axis (at the focal point). Now you want to know which focal length you need. Divide the FOV by 2 (= 0.5 degree), take the tan value (= 0.008727), and divide the radius by this (5 / 0.008727 = 573 mm). The necessary focal length is thus 573 mm.
The famous Andromeda galaxy has a size of 160 x 40 arc seconds. This is one of the biggest deep sky objects. The famous whirlpool galaxy (M51) has a size of 10 x 5.5 arc seconds. This is more of a typical size for deep sky objects.
The usable magnification is determined by the mirror diameter. The actual magnification is determined by dividing the focal length of the main mirror by the focal length of the eyepiece. See formula below.
Eyepieces with a focal length below 8 mm tend to be difficult to look into for some observers. Eyepieces are readily available with focal lengths of about 5 - 50 mm. Eyepieces with very short and very long focal lengths are more expensive than the middle range.
The focal ratio is the focal length divided by the main mirror diameter. This number is usually expressed as f/n, where n is the ratio number. Although it is sometimes written as fn, this should be considered a wrong notation.
The effective focal ratio of a mirror - eyepiece combination is :
Note : The formula for the effective focal ratio may be an approximation, only valid for the small angles we are working with. (i.e. < 1 degree). If you know anything about this, please mail me.
A scope is called fast if the focal ratio is a small number (i.e. f/5), it is called slow if the focal ratio is a high number (i.e. f/8). When selecting a focal ratio for your scope to be you should be aware of the following optical considerations.
The amount of light received from a single object depends only on the aperture of the scope, i.e. the mirror diameter. (Minus the secondary)The FOV in the primary focus of the scope depends only on the focal length of the main mirror. (In other words; the size of an object in the primary focus depends only on the focal length)
It is generally said that you need a 'fast' scope for imaging. This is of course only true if you need the bigger FOV that comes with the 'fastness'. E.g. if your main purpose is planet imaging a slow scope may be advantageous since it makes using eyepiece projection a little bit easier.
The size of the secondary is important for the contrast in the scope (see 'Obstruction' in "The Secondary Mirror"). Slower scopes can use a smaller secondary and thus can achieve a better contrast. This is the reason why they are often the preferred scopes for planetary observations.
For terrestrial observations, the focal plane can be found with the following formula :
Non-optical factors when choosing a focal length :
- Longer focal lengths are easier to grind as short ones.
- The longer the focal length, the more difficult to build the scope (mechanically speaking).
- For very long focal lengths, beware of the eyepiece height above ground when observing in the zenith. (You may need a ladder to get to it!)
- If your scope has to be transportable, check what the maximum length is that you can transport.