There is a cut-off frequency above which the equation cos ⁡ ⁡ θ θ = 1 / ( n β β ) can no longer be satisfied. The refractive index n varies with frequency (and hence with wavelength) in such a way that the intensity cannot continue to increase at ever shorter wavelengths, even for very relativistic particles (where v / c is close to 1). At X-ray frequencies, the refractive index becomes less than 1 (note that in media, the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below the frequencies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonant frequency (see Kramers–Kronig relation and Anomalous dispersion).