Calculating the energy and intensity of Cherenkov radiation involves understanding the relationship between the particle's velocity, the refractive index of the medium, and the emitted radiation's wavelength. The threshold for Cherenkov radiation occurs when a charged particle travels faster than the speed of light in a given medium. The intensity can be derived using the Frank-Tamm formula, which relates the intensity to the particle's charge, velocity, and the refractive index. The energy of the emitted radiation can be calculated using the formula E = (q^2 / (4πε₀)) * (1 - (1/n²)), where q is the charge of the particle and n is the refractive index. Understanding these calculations is crucial for applications in particle physics and astrophysics.