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Galileo's method to measure the magnification of a telescope

by Philippe Jeanjacquot last modified Jul 13, 2012 03:37 PM

Galileo’s method

In 1610, when Galileo observed the sky with his telescope the stars seem to be closer. In fact, the telescope has a magnification. For example, he wrote “At first I looked at the Moon from so close that it was scarcely two terrestrial diameter”(Sidereus Nuncius)

In his book “Sidereus Nuncius”(Sidereal Messenger) Galileo gave an experimental approach to measure his telescope magnification.

He draw two circles (or two scares) the diameter or the length of the second is twenty times smaller than the first. The objects were fixed on the same wall far from the observer. The observer watches the first to the naked eye and the second with the other eye across the telescope. If the magnification is twenty, both circles of squares seem to have the same size.

Diagram from Sidereus Nuncius
Diagram of magnification measurement from Sidereus Nuncius

Our students method

From this approach our students build their own method to measure the telescope magnification.

We take 2 objects with the same size (for example 2 pieces of paper). One piece of paper was put at a great distance of the telescope (about 40m). With one of his eyes he observed the object through the telescope. He wrote the distance between his eye and the piece of paper

A distance: dA=………………..m

Our partner take the other piece of paper and stand with the paper in his hand in front of the telescope. We observe the object with our other eye.

So with one eye we see the first objet through the telescope and with the other we see the second object without the telescope.

Our partner moves still the second object seems to have the same size as the other.

We write the distance between the second object and our eyes.

B distance: dB=………………..m

Experiment in our school 1 Experiment in our school 2

On the picture above we can see the first piece of paper stick on a window of our school the distance between the paper 1 and the telescope is dA=44m



On the picture above we move the piece of paper two until we see it with the same size that the image of the paper 1 across the telescope. We find dB=0,95m



What we can see in our telescope Our experiment in Roma
Piece of paper 1 image across the telescope. Our experiment during a European Comenius meeting in Scuola Secondaria di 1' grado G.G.Belli in Roma in this case: dA=62m and dB=1.2m

Calculations for our experiments

We use this formula to find the magnification: Magnification formula 0

In our school we found: dA=44m ; dB= 0.95m; Magnification=44/0.95=46

In Roma we found: dA=62m ; dB= 1.2m; Magnification=62/1.2=52

How to find the formula (theory)

Magnification calculations

Another way to calculate magnification

Nowadays, we know how to calculate a telescope magnification we have to find on the telescope the objective focal length and the eyepiece focal length

Magnification formula 2

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