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## Homework Statement

A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam.

## Homework Equations

Focal ratio, R = focal length, f / Diameter, D

## The Attempt at a Solution

To create a f/10 beam using the 50mm lens, R = f/D so 10 = f / 50, making f = 500mm. This doesn't sound right at all, as it doesn't take into account the telescope's f/7.5 ratio or the fact the lens is 150mm away from the unmodified focal plane. I feel like I'm missing some other equation or important piece of this problem.