Understanding Angular Magnification in Simple Magnifiers and Telescopes

[ThatDude]

So basically, in the text below, they say that maximum angular magnification is achieved when the object is placed 25 cm from the eye, i.e. at the near point. The minimum angular magnification is achieved when the object is placed at the focal length.

However, for the chapter on the telescope, they explain that to achieve maximum angular magnification, you need the image at infinity, therefore the object must be at the focal length!

Is this not contradictory?

 

[RaulTheUCSCSlug]

I think you may be confused on the difference between the telescope and the magnifier. The highest angular magnification still occurs at the eye's focal point, which would be at the focal point of the eye piece of the telescope, the object lens on the telescope is what needs to see the image at infinity. Please note that these are also "Mickey Mouse" equations that only deal with special scenarios and thin lens, because a real lens will have some type of aberration, and the better telescopes will use a parabolic-reflector which offers no aberration (a simple derivation of this would be a good exercise as I did it yesterday and was quite fun!)

 

[RaulTheUCSCSlug]

Also think about what happens when an image is infinitely far away, using Pythagoras theorem we see that the object is very very tall, but judging it from very far we can also use a small angle approximation.