Okay. I understand that the question doesn't focus on the spectrometer, but I'm still pretty sure that I need to understand how the setup would work in order to make any progress. If I could just get a text diagram of how the device would look, like so:
telescope lens--extra lens--focal...
Homework Statement
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...