# Focal Length, Wavelength Relationship

I have a cylindrical lens with a design wavelength of 587.6nm. The radius (S2) of the lens is 2mm, and the radius of the opposite face (S1), i assume is 0mm.

The focal length is given as 3.91mm and the back focal length is given as 1.4mm.

If I am using a wavelength of 905nm.

The question is how do I calculate the change in focal length of the lens due to the increase in wavelength. I have read many articles that seem to relate the lens equation and something called cauchy equation but I couldn't see anything that made sense to my non-optic way of thinking.

thank you in advance ddB

## 1 Answer

The focal length will depend on the index of refraction of the used material, and that is a material-specific function of the wavelength of light. This function is related to the "dispersion relation" of that material. It may be approximated by a linear relationship within the narrow band of visible light. Often, longer wavelengths lead to lower index of refraction, in which case we speak of normal dispersion. But there are exceptions, and over larger bands of wavelengths, the dispersion relation may exhibit resonances or the material may become opaque. So in short, your question is not answerable without additional information.