# Telescope & Eyepiece Calculator Spreadsheet

Updated 21.01.2012 - version 1.3

This calculator is a spreadsheet created in microsoft Excel. Its purpose is to calculate useful parameters for telescopes and eyepieces, help organizing an eyepiece collection and lists several useful optical formulae. It features the following calculations:

- Limits for focal length of an eyepiece based on: exit pupil, aperture, focuser diameter, eyepiece field of view, etc.
- Calculator for eyepiece collection and guidelines for choosing eyepieces.
- Apparent magnitude and suface brightness of a given deep sky object, as observed through telescope at different magnifications.
- Instrument resolution, field of view, observable magnitude, magnification, etc.
- Graphs and charts of these parameters as a function of magnification.
- Comparison of two telescopes
- Formulae used for calculations are included

## Download:

Telescope Calculator spreadsheet(Excel 2003, 500KB, Version 1.3)

Eyepiece Collection calculator (Included in "Telescope Calculator")

Note: These calculators require Mirosoft Excel 2003 or later to open. A free Excel reader can be downloaded from this site.

## Screenshots:

Telescope calculator section

Eyepiece collection calculator section

Generated graph of apparent object magnitude

## Note About Surface Brightness:

One of the purposes of this calculator is to bring attention to a topic often unfamiliar to amateur astronomers: The fact that apparent surface brightness (intensity per area of our retina as we see it) of extended deep sky object never actually increases, no matter which telescope or eyepiece we shall use.

Assume we observe Andromeda galaxy
with our naked eyes. There is a certain amount of light denisty (per square metre) falling on our eye's retina - irradiance if we use radiometric therminology, or we may simply call it apparent surface brightness.

If we take a telescope and use magnification which gives us brightest possible image (exit pupil equals to dark adapted eye's pupil which is approximately 6-7mm) There will be no change in apparent surface brightness of the object, meaning Irradiance on our retina will stay the same. A mathematical proof to this is included in attached Excel file, though it can simply be backed by "Radiance Conservation Law" or "Extent Conservation Law" which is ultimately a conservation of energy.

It should be realized though, that there are other factors involved which allow us to see the object through the telescope: Contrast does increase with magnification (due to lower sky glow), Size also increases, so is the overall apparent magnitude.

This is illustrated in attached graph (screenshot above): The red chart represents apparent magnitude, and the blue one represents apparent surface brightness. Chart plotted as a function of magnitude, and we can note that higher values correspond to s lower brightness.

The breaking point on the chart shows magnification at which telescope's exit pupil equals to human eye pupil (6-7 mm). Under this magnification we begin to lose light, even though apparent surface brightness does not change. Over this magnification we lose the apparent surface brightness (but overall magnitude will remain constant).

Bottom line: If we want to use really low magnification - we can do it, if the goal is to fit object into field of view. But in this case observer's pupil will clip the effective aperture and some light will be lost (though it still will be brightest possible image at given magnification).

It is a better to use a smaller aperture instrument for this purpose, or to add an aperture mask to decrease the exit pupil to 6-7mm diameter.