1. The problem statement, all variables and given/known data From Optics by Frances Sears, 1949, Chapter 6, Problem 11: (I've been working all the problems in the book on my own.) A crude telescope is constructed of to spectacle lenses of focal lengths 100cm and 20cm respectively. (a) Find its angular magnification. (b) Find the height of the image formed by the objective of a building 200ft high and distant one mile. 2. Relevant equations Part a is straightforward. Angular magnification of a telescope = -f1/f2, where f1 is the focal length of the objective and f2 that of the eyepiece (ocular in Sears' language). So I got -5x, which matches the back of the book. I don't know what the relevant formulas are for part b, that is part of the problem. 1/p+1/q = 1/f, of course, and lateral m = -q/p = y'/y. The book claims the answer is y'=1.49 inches. I have no idea where they got that. Sears gives angular magnification as tan u' / tan u, where u' and u are the angles subtended with and without the instrument. 3. The attempt at a solution tan u = 200 ft/5280ft, where u is the angle subtended without the telescope. so tan u = .0379 rad. u' is the angle subtended with the telescope in use, so with -5x angular magnification, I would think that would make tan u' = .1916 (approximating u=tan u and u' = tan u'.) The real problem is, I have no idea where the final image is supposed to be. In some problems, the final image is supposed to be at infinity (not that they ever SAY so) but that would make no sense here. I tried to brute force it by finding the image of the first lens, use that as the object of the second lens, and find the final image, and with it the lateral magnification. Unfortunately, that requires me to know the spacing of the lenses, which is NOT given. Again, when looking at infinity I get the general idea that the focal points should overlap so the separation of the lenses should be the sum of the focal lengths, 120cm. However, that gives me a final image height of -40.3 ft, while Sears claims 1.49 inches is correct. I am clearly missing a piece of information, or an assumption I am supposed to make. This is getting frustrating as I have tried Wikipedia and other optics texts and they all get a little bit vague and hand-wave when it comes to this point. I actually took up optics this summer because I got sick of it being the only topic in intro physics I have trouble teaching to my students. Microscopes and telescopes both are frustrating. This should be simple. I'm getting nearly every odd problem right in the text (it has odd answers in the back), but I finally get to the point I really wanted to know, and I'm STILL stuck. Help?