The Swiss mathematician Johann Heinrich Rahn studied under John Pell in Zurich in the 1650s. Prompted by Pell (who worked on a revised version of Rahn's treatise on algebra, which was published in London in 1668), Theodore Haak made contact with Rahn in 1671, and received a letter from him describing his recent work on optics. This letter was passed on to Henry Oldenburg, who, with the assistance of John Collins, composed a lengthy reply, surveying recent scientific and mathematical publications. Significantly, however, Oldenburg did not consult Pell, even though this correspondence arose in the first place from Pell's friendship with Rahn; the reason for this omission was that Oldenburg and Collins hoped that Rahn could supply details of Pell's mathematical methods that Pell himself was refusing to divulge. Oldenburg's letter is published here for the first time.