Northern Stars Planetarium

How to calculate a telescope's
magnifying power and f/ratio

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Magnification:

You can change the magnifying power of any telescope by simply changing the eyepiece. Different eyepieces have different focal lengths, the shorter the focal length of an eyepiece, the higher the magnification it will provide. However the eyepiece is not set at a given magnifying power, because its magnifying abilities are dependent upon the objective lens. So an eyepiece that provides a 16X magnifying power on one telescope, may provide a 50X magnifying power on a different telescope; it's all dependent upon the focal length of the given telescope's objective lens or mirror.

To calculate the magnifying power of any telescope you simply divide the focal length of the objective lens or mirror by the focal length of the eyepiece. Remember to use the same measuring units, eyepieces are generally sold by their focal length in millimeters, telescopes are often sold by their focal lengths in centimeters or inches. Don't forget to convert first!

Magnification=Focal length of the Objective/Focal length of the Eyepiece
OR

M = Objective f.l./Eyepiece f.l.

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A Magnifying Challenge!

Let's say we have three telescopes. One is a Catadioptric type of telescope with a primary mirror that is 8" in diameter and has a focal length of 2000 mm. The second scope is a Refracting telescope that has a primary lens that is 60 mm in diameter and has a focal length of 800 mm. The third telescope is a Reflecting telescope that has a primary mirror that is 4" in diameter and has a focal length of 450 mm.

We have three eyepieces too. Each has a different focal length. The lengths are: 8 mm, 12 mm, 26 mm.

Can you calculate the various magnifying powers of the three telescopes described and how they will vary depending on which eyepiece you use?

for answers...	8 mm f.l. eyepiece	12 mm f.l. eyepiece	26 mm f.l. eyepiece
Catadioptric 2000 mm f.l. 8" diameter	?	?	?
Refractor 800 mm f.l. 60 mm diameter	?	?	?
Reflector 450 mm f.l. 4" diameter	?	?	?

Remember: M = Objective f.l./Eyepiece f.l.

 

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f/Ratio: The f/ratio of a telescope is determined by dividing the focal length of the primary lens or mirror by the aperture (the diameter of that same lens or mirror). This number tells us several important things about a telescope. For example, the lower the f/ratio the faster the telescope is said to be; that basically means that it provides a brighter image than a similar sized telescope with a higher f/ratio. Yet, remember that there is always a tradeoff, by getting brighter images you loose some magnifying power. Telescopes with low f/ratios give wide-field images with bright star fields, they are good for viewing star clusters and faint nebulae. Telescopes with high f/ratios aren't quite as bright, but yield higher magnifications with narrower fields of view. They are ideal for planet viewing and splitting binary stars.

f/6 and lower would be considered fast, ideal for viewing faint nebulosity and wide field objects.

f7 to f/10 would be midrange. The compromise range, telescopes with f/ratios in this range do fairly good at both ends.

f/11 and up would be considered slow, but ideal for planetary work or studying binaries.

Again, when calculating f/ratios, remember to use the same units of measure. Don't divide centimeters by inches!

*AN IMPORTANT POINT* Remember that using f/ratios to compare two telescopes works best when things are equal otherwise. A 10 inch f/11 may very well give you much brighter images than a 4 inch f/6 because it has more light gathering abilities with it's greater aperture. A safer comparison would be comparing two telescopes of the same aperture, but with different f/ratios.

• 1. Which would provide a brighter image an 8 inch f/10 or an 8 inch f/6?
  
• 2. Which would provide more magnification, a 6 inch f/8 or a 6 inch f/5?
  
• 3. Which would provide a wider field of view a 4 inch f/6 or a 4 inch f/4?

Using the same three telescopes as above, calculate their f/ratios. Which one would be best for planetary studies? For studying nebulae?

Telescope	Focal Length	Aperture	f/ratio
Catadioptric	2000 mm	8 inches or 203 mm	?
Refractor	800 mm	60 mm	?
Reflector	450 mm	4 inches or 102 mm	?

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Northern Stars Planetarium and Educational Services,

Fairfield, Maine 04937
(207) 453-7668
info@northern-stars.com  

• 1. An 8 inch f/6 would provide brighter images than an 8 inch f/10.
• 2. A 6 inch f/8 would provide greater magnification than a 6 inch f/5.
• 3. A 4 inch f/4 would provide a wider field of view than a 4 inch f/6.