# How does a Galilean telescope form an enlarged image even though it has a diverging lens?

I have been reading about Galilean telescope and the picture in the book is something like this:

After rays pass through the converging lens, there is a real image formed which is intercepted by the diverging lens but as I learnt before, diverging lens cannot form an enlarged image. So, is the ray diagram inaccurate?

• Does the book say something about the A'B' arrow? I don't understand what it could mean. From my point of view, the rays emerging from the diverging lens seem to come from a virtual image PQ Commented Jan 2, 2017 at 18:51
• the A'B' arrow is the image formed by the converging lens if there was no diverging lens in between which would become the image for the diverging lens when it intercepts the rays coming from the converging lens Commented Jan 3, 2017 at 5:04
• please try to post further information, maybe an extract of the book from which it is taken where it is explained. Commented Jan 4, 2017 at 19:30
• It is a sub-topic of the lesson "geometrical optics" There is not much information except the derivation Commented Jan 5, 2017 at 9:46

The angular magnification of a telescope $$M$$ is defined as the ratio of the angle subtended by the image of the object when looking through the telescope $$b$$ to the angle subtended by the object when looked at with the unaided eye $$a$$.

$$M=\dfrac ba$$

Those angles are often called visual angles and they detained the size of the image which is formed on the retina.
The bigger the visual angle, the bigger the image formed on the retina and the bobber the “object” being viewed is perceived to be.

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I have annotated your diagram which clearly shows that $$b>a$$ which means that the angular magnification of such a telescope is greater than one ie the Galilean telescope magnifies.

The final image can be formed at infinity as shown in the ray diagram below.

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$$f_1$$ if the focal length of the convex lens which converges the incoming rays and $$f_2$$ is the focal length of the concave hens which diverges the incoming rays.
Again the visual angle for the final image $$u’$$ is greater than the visual angle for the object being observed $$u$$.

• It is given in my book that, for normal adjustment, $A'B'$ is at the focus of the concave lens and the image $PQ$ forms at infinity. How is this possible? It seems to behave like a convex lens. Using ray diagram, I figured out the image should form at the midpoint of the object and the optical centre. Commented Dec 30, 2019 at 9:09
• @M.GuruVishnu I have added a ray diagram to illustrate how the final image can be formed at infinity. Commented Dec 30, 2019 at 9:41
• Thank you very much. Now I understood how image formation takes place at infinity. The diverging lens diverges the convergent beam to give a parallel beam which is interpreted as an image at infinity by the observer (Am I right?). But my original doubt still exists. Could you please look at this ray diagram I constructed. I find no error in that. But it can be seen the image is formed at the midpoint of focal length on the same side of object (image formed by the convex lens). I also verified it using the thin lens formula. Could you please clarify this? Commented Dec 30, 2019 at 10:17
• For those having the same doubt as of mine as discussed in the comments above : How does a diverging lens in a Galilean telescope form an image at infinity when its object is at its focal plane? Commented Jan 4, 2020 at 11:22

There is your answer, the Galilean telescope - the assembled telescope as a whole with EVERY component part of it in its correct place - magnifies.

But you did raise a concern in your question that a diverging (or concave) lens cannot form an enlarged image. That is also correct. Such a lens, standing alone, a single component not in a telescope and not in conjunction with another lens -indeed cannot magnify.

This is probably a poor simile, but a car wheel by itself cannot move, it will just sit where you happen to leave it. But put it in its correct place with other component parts, in this case called a "car", and that wheel suddenly has the capability of movement.

Sometimes, things can work only when they work together.

I think that perhaps the ray diagram in this article https://thesciencegeek.org/2018/03/13/galileo-and-the-telescope/ is perhaps easier to follow. It shows clearly how the angular magnification is achieved. The article provides useful background