# Number of modes in a cavity

This might be a bit to specalised for some of you, but i am trying to calculate the number of modes that light can propegate in a material. The question is as follows

Consider a cavity that is a cube with the side length a = 1mm filled with water (refractive index(n) 1.33). Calculate the number of cavity modes that fall withing a bandwidth Delta f = 1MHz at the frequency of Ar laser (vaccume wavelength 488nm)

Now, we have been taught the equation that the numer of modes N in the material, N = (8Pi * n^3 * a^3 8f^3) / 3 c^3 where c is the speed of light in vaccume.

We have also been taught that The number of modes in a frequency interval between f and delta f is given by DeltaNf = (dNf/df)Deltaf

I get an answer of 827 modes in that interval. I got the frequency by using f=c/landa in the vaccume and remembered that the frequency of light is the same in every medium. (6.1475x10^14 Hz) Is this the right frequency to use in the water? And am I calculating the number of modes right?