![]() Actually, I like exit pupils of at least 1.0mm for decent viewing.Įxit pupil can be calculated by dividing the telescope's clear aperture (in millimeters) by the magnification produced by the ocular in use. Exit pupils of less than about 0.5mm are so small and pass so little light to the eye that they are functionally useless. On the other hand, as the exit pupil decreases below 7mm, lack of light becomes the basic limiting factor to what you can see at night. The pupil of fully dark-adapted human eye can dilate to about 7mm diameter, so an exit pupil in excess of 7mm is passing more light than the eye can accept. The exit pupil is the diameter of the "light pencil" that emerges from the eyepiece. Thus:įor example, a 100mm clear aperture is approximately 4", so such a telescope operating at 100x magnification is at 25 PPI (100/4=25). PPI can be calculated by dividing the magnification of the telescope and eyepiece combination by the telescope's clear aperture in inches (1 inch = approximately 25mm). In average seeing conditions, I figure about 30 PPI as a practical maximum. This is good to know, because it is a truism among amateur astronomers that the power per inch (PPI) figure of a telescope and ocular should not exceed 50 PPI in excellent seeing conditions. I do not know which method is more accurate, but both are close enough for practical purposes. The results produced by the two formulas are very similar, but not quite identical. Used in our 1000mm focal length telescope this formula produces a FOV of slightly over 1.2 degrees (21.2 / 1000 = 0.0212 × 57.3 = 1.21476). OCULAR FIELD STOP DIAMETER / TELESCOPE FOCAL LENGTH x 57.3 = FOVĪ Tele Vue 25mm Plossl has a field stop diameter of 21.2mm. Unfortunately, most ocular manufacturers do not provide a field stop diameter for their eyepieces one company that does is Tele Vue. The other formula for calculating FOV in degrees involves dividing the eyepiece field stop diameter by the prime focal length of the telescope and multiplying the result by the constant of 57.3. The true field of view is therefore 1.25-degrees (50/40=1.25). Used in a telescope with a 1000mm prime focal length, the magnification is 40x. Thus:įor example, a 25mm Plossl eyepiece generally has an AFOV of 50-degrees. The AFOV for almost all eyepieces is provided by the manufacturer and it is easy to derive the magnification of any telescope/ocular combination. The easy way and the method I use is to divide the apparent field of view (AFOV) of the ocular by the magnification of the system. There are two ways to calculate the true field of view (FOV) in degrees of a telescope and eyepiece combination. Always make sure you're using the same units! True Field of View TELESCOPE FOCAL LENGTH / CLEAR APERTURE = FOCAL RATIOįor example, a telescope with a focal length of 1000mm and a 100mm (4") clear aperture has a focal ratio of f/10 (1000/100=10).Īn example calculation of focal ratio and magnification for a scope with a 25 mm focal length, eyepiece, 102 mm aperture, and 900 mm focal length, telescope. In other words, the focal ratio is the ratio of the focal length and clear aperture. The focal ratio, or f/stop, of any lens system (including telescopes), is computed by dividing the focal length by the clear aperture (usually expressed in millimeters). TELESCOPE FOCAL LENGTH / OCULAR FOCAL LENGTH = MAGNIFICATIONįor example, a telescope with a 1000mm focal length using a 10mm ocular is operating at 100x magnification (1000/10=100). It is calculated by dividing the focal length of the telescope (usually marked on the optical tube) by the focal length of the eyepiece (both in millimeters). The magnification of an astronomical telescope changes with the eyepiece used. To illustrate the various formulas below, I will use a telescope with a 100mm (4") clear aperture and a prime focal length of 1000mm. If they are not, the manufacturer's web site usually has the basic numbers, as should the instrument's Owners Manual. Most of the values you need to know to work these formulas, such as prime focal length, focal ratio and clear aperture, are usually printed right on the optical tubes of astronomical telescopes, binoculars and the barrel of eyepieces. (Binoculars are just two small telescopes linked together, so the same formulas work for them, too.) Armed with a simple calculator and the following formulas, even I can work out the vital statistics of my telescopes and eyepieces. However, sometimes it is good to know how to calculate some of the numbers commonly mentioned by telescope owners and in telescope articles. I am about as far from being a mathematician as it is possible to get.
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