Magnification

11.23 - Be able to use the formula for the magnification of a telescope:
fo = magnification
fe
where fo is the focal length of the objective element and fe is the focal length of the eyepiece

Magnification depends on the focal length of the telescope and the focal length of the eyepiece.

Focal Length is how far light travels inside the telescope before it reaches a focus point.

My Cassegrain Schmidt Telescope has a focal length of 1470mm which is roughly a meter and a half. The light uses a secondary mirror inside to reflect the light inside and so uses its size intelligently.

Eyepiece Focal Length works in the same way so for example I have a short 9.7mm and a longer 40mm eyepiece. I will experiment using different eyepieces when looking at a planet to find the best one and use a different eyepiece for the Moon than I would the Orion Nebula.

So why don’t astronomers use the highest magnification possible all the time? Look at the image of Saturn on this page. A low magnification may produce the smaller image but it is the sharpest and most defined. Too much magnification can be as unsatisfactory as too little.

An inverse relationship exists between magnification and the field of view so that a smaller eyepiece will produce a higher magnification.

Magnification = Telescope Focal Length / Eyepiece Focal Length

Telescope Focal Length = 1470mm. Eyepiece Focal Length = 40mm.
1470 divide 40 = 36.7 x Magnification

Using the same Telescope what is the magnification for each of these eyepieces?

Question 1

Eyepiece Focal Length of 20mm

1470/20 = 73.5 x Magnification

 

Question 2

Eyepiece Focal Length of 9.7mm

1470 divide 9.7 = 151.5 x Magnification

 

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Summary

Magnification =
  fo (Focal length of the objective element)  
fe (Focal length of the eyepiece)

Links

Starizona Observing Theory

Highlands Astronomical Society Telescope Basics

Astronomy Tools Magnification/Eyepiece Calculator

Astronomy Tools Focal Length Calculator