Chromatic focal shift is used to characterize the variation of focal wavelength of optical system with wavelength. It
is an important tool and index to analyze the color difference of optical system. In this paper, the function relationship
between focal length and wavelength of optical system is analyzed by using chromatic focal shift. According to the
dispersion characteristics of the optical system material, the Conrady formula which fits the refractive index curve well
with less data is selected. Simulations show that the chromatic focal shift of most of monochromatic wavelength systems
in the 400-1000 nm wavelength range is monotonically increasing and can be expressed by the Conrady dispersion formula.
The chromatic focal shift of achromatic systems which consists of a variety of glass materials usually has an inflection
point, and the shapes of most of the achromatic chromatic focal shift are the same, so the formula for the curve should be
consistent.The calculation results show that the Conrady formula can also solve the curve of the achromatic system
effectively in a relatively short band, such as 400nm~700nm. In fact, the chromatic aberration correction of most
achromatic systems is limited, and the effective working band is short. Therefore, the Conrady formula is a very good
expression for both monochrome and achromatic systems. By studying the chromatic focal shift analytical equation of the
optical system, it provides a reference for the theoretical calculation and detection of focal length at a specific wavelength.