The de Broglie equation, λ = h/p = h/(mv), relates the wavelength (λ) of a particle to its momentum (p) and Planck's constant (h). This equation is applicable to particles with both mass and momentum, including those in various mediums.
However, it's important to note that the equation you mentioned, f = mc^2/h, is not the de Broglie equation. The equation you provided seems to be attempting to relate the frequency (f) of a particle to its mass (m) and the speed of light (c), but it is not a valid equation within the context of de Broglie's work or special relativity.
In de Broglie's theory, the wavelength of a particle is related to its momentum, not its mass. The de Broglie wavelength is given by λ = h/p, where p is the momentum of the particle. This equation holds true for particles in vacuum as well as in other mediums.
The speed of light, denoted by 'c', is a constant that represents the speed of light in a vacuum. In other mediums, the speed of light can be different, typically slower than the speed of light in a vacuum. If you're dealing with particles in a medium, you would need to consider the appropriate speed of electromagnetic waves in that particular medium, rather than using the value of 'c' for the speed of light in a vacuum. The appropriate speed of electromagnetic waves in a medium is denoted by 'v' or 'c_m' (the speed of light in the medium).
To summarize, the de Broglie equation, λ = h/p, is valid for particles in both vacuum and other mediums. When dealing with particles in a medium, you would replace the speed of light 'c' with the speed of electromagnetic waves in that medium, denoted as 'v' or 'c_m'.