1. The problem statement, all variables and given/known data A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires an f/10 beam at its input. Compute the focal length of a 50mm diameter lens that, when inserted in the beam 150mm in front of the unmodified focal plane, produces the required beam. 2. Relevant equations Focal ratio = focal length/diameter of entrance aperture. The notation f/10 means that the focal ratio is 10, not that the diameter is 10. 3. The attempt at a solution I tried drawing some diagrams, which obviously can't be reproduced with ease here. I think the main problem might be that I'm not familiar enough with telescopes to know how one uses a spectrometer or an extra lens--must they go outside the telescope, thereby making the focal length longer, or can one or both be placed inside the telescope? I also tried making up variables--saying, for instance, that the telescope's original focal length is 750 and its entrance diameter 100, which fits for f/7.5. But then I was stymied by the above fact: I don't know how a spectrometer works. I think if someone can give me information about the mechanics of the problem I should be able to make a better attempt. Thanks.