Okay so I want to solve for refractive index. I'm given the dielectric constant and the permeability M. From what I understand the refractive index is frequency dependent. I'm just unsure what equation to use. n=(Er)^1/2 does not work because the dielectric constant for water is 80.1 and the known index is 1.333. what do I use??

To calculate the refractive index of a medium using the dielectric constant (εr) and permeability (μ), you can use the equation:

n = √(εr * μ)

However, this is the equation for the refractive index in the absence of dispersion, meaning it assumes that the refractive index is independent of frequency. In reality, the refractive index of a material is often frequency-dependent, which means it can vary with the wavelength or frequency of the light passing through it.

To account for the dispersion of the refractive index, you need to use a more generalized equation. One commonly used equation is the Cauchy equation:

n = A + (B/λ^2) + Cλ^2

In this equation, n is the refractive index, λ is the wavelength of light, and A, B, and C are coefficients that depend on the material. The Cauchy equation allows you to calculate the refractive index at different wavelengths by adjusting the values of λ and the coefficients A, B, and C.

Keep in mind that the values of the coefficients in the Cauchy equation will be specific to the material you are working with. If you have the dielectric constant and permeability for a material like water, and you know the refractive index at a specific frequency or wavelength, you can use this information to determine the values of A, B, and C in the Cauchy equation for that specific material.