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Introduction |
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Terms & Symbols |
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Scope Equations |
Stars are so unimaginably far away that the light we receive from them arrives in rays that are perfectly parallel. Your eye is designed to focus these parallel rays to a point, allowing you to identify where the light is coming from.
A telescope, in its original configuration (refractor), consists of two lenses. The first one, the objective lens, collects light and focuses it to a point. The second lens, the eyepiece, catches the light as it diverges away from the focal point and bends it back to parallel rays, so your eye can re-focus it to a point.
Notice how the telescope has taken all the light passing through the objective lens and compressed it down to a column of light that will pass through the pupil of the eye. This is one of the three major tasks of the telescope, the full list being:
The equations on this page permit you to find just exactly how well the telescope will perform these tasks, and along the way I also show how the tasks are accomplished, by explaining both the theory and the practice.
| Symbol | Meaning |
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| Dep | Diameter of the exit pupil. The exit pupil is where the light leaving the eyepiece converges to its smallest circle -- you find the exit pupil when you bring your eye up to the eyepiece until you can see the whole image. |
| DO | Diameter of the objective. The "objective" can be either the large lens at the front of the telescope (in a refractor) or the large mirror at the back of the telescope (in a reflector). |
| fe | Focal length of the eyepiece. The distance from the center of the eyepiece lens at which light passing through the lens is brought to a focus. |
| fO | Focal length of the objective. The distance from the center of the objective lens (or mirror) at which incoming light is brought to a focus. |
| fR | f-Ratio. Simply the ratio of the focal length to the diameter of the objective, or fO/DO. This is written "f/" and then the value. An example would be an "f/10" telescope, meaning the focal length is 10 times the diameter of the objective. This is commonly given along with the diameter of the objective to describe a scope, and is a surprisingly useful parameter for characterizing its performance, as seen below. |
| FOVe | Field of view of the eyepiece. The angle across which you can see when looking through the eyepiece alone. The two parameters fe and FOVe are the two primary specifications for the eyepiece. |
| FOVscope | Field of view of the scope. Tells you how much of the sky you see in the image in the telescope. This is the distance from one side of the eyepiece image to the other, expressed in degrees or minutes of arc across the sky. |
| Gmag | Gain in visible star magnitudes. The increase in star magnitudes that you can see by looking through the scope (compared to looking by eye). So for example if the faintest star you can see by eye is magnitude 5, a gain of 7.3 would mean you could see stars of magnitude 5+7.3 = 12.3 in the scope. |
| M | Magnification. The apparent increase in size of an object when looking through the telescope, compared with viewing it directly. |
| PR | Resolving Power. The smallest separation between two stars that can possibly be distinguished with the scope. This is an indication of the finest detail the scope is capable of seeing -- regardless of the magnifying power. |
| Term Computed | Equation | Theory & Practice |
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| Resolving Power (in arcseconds) |  |
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| Magnification |  |
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| Scope Field of View |  |
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| Minimum Magnification |  |
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| Max Eyepiece Focal Length |  |
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| Maximum Magnification |  |
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| Min Eyepiece Focal Length |  |
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| Gain in Visible Star Magnitudes |  where 7 = diameter of pupil of the eye in mm. |
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| Surface Brightness at Magnification M using Eyepiece Focal Length fe |
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Your questions and comments regarding this page are welcome.
You can e-mail Randy Culp for inquiries,
suggestions, new ideas or just to chat.
Updated 25 November 2009
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