In the course of either buying or using a telescope, it would be nice to know how much more powerful the telescope is than your eye in gathering light. You would also like to have an idea of what the faintest magnitude you can see would be.
The following Java applet can answer these two questions for you. Before proceeding, please note that all numbers used are metric. First, you need to provide the size (diameter) in millimeters of the pupil of your eye. From this, you can determine the surface area of your eye that is used to collect light. The average maximum pupil diameter is between six and seven millimeters. As you age, the maximum diameter the pupil can attain shrinks. For a 50 year old, the pupil will probably expand to a diameter of no more than five millimeters.
Next you need to specify the faintest magnitude star you can see with your naked eye. This is called the Limiting Naked Eye Magnitude. For the best viewing conditions, this value can be as small as 6th magnitude. For a viewer in an urban area, a value of 4th magnitude is not unusual.
The final number the applet needs is the diameter of the telescope you want to analyze. Note that this number is taken to be clear aperture. This means that if you are sizing for an 8 inch (200 millimeters) telescope, it is assumed that the telescope has a full 8 inch diameter lens/mirror. In the case of the various types of reflecting telescopes, no subtraction is made for the central obstruction.
Please note that this simulation makes no allowance for inferior optics and is an idealized solution. Based on the numbers provided, the applet will tell you the Light Gathering Power multiple of the telescope vs your naked eye. This number is based solely on the difference in total surface area of your eye vs the telescope.
The applet will also give an approximation of the magnitude of the faintest point source of light that you should be able to see with a telescope of the specified diameter.
I hope you find the following applet to be both fun and educational.
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