  The Epoch of Reionization Spectrometer (EoR-Spec) will be an instrument
module for the Prime-Cam receiver on the CCAT-prime Collaboration's Fred Young
Submillimeter Telescope (FYST), a 6-m primary mirror Crossed Dragone telescope.
With its Fabry-Perot interferometer (FPI), EoR-Spec will step through
frequencies between 210 and 420 GHz to perform line intensity mapping of the
158 $\mu$m [CII] line in aggregates of star-forming galaxies between redshifts
of 3.5 and 8 to trace the evolution of structure in the universe during the
epoch of reionization. Here we present the optical design of the module
including studies of the optical quality and other key parameters at the image
surface. In order to achieve the required resolving power (R$\sim$100) with the
FPI, it is important to have a highly collimated beam at the Lyot stop of the
system; the optimization process to achieve this goal with four lenses instead
of three as used in other Prime-Cam modules is outlined. As part of the
optimization, we test the effect of replacing some of the aspheric lenses with
biconic lenses in this Crossed Dragone design and find that the biconic lenses
tend to improve the image quality across the focal plane of the module.
