Conical diffraction occurs when light is incident along the optic axis of a biaxial crystal. The light spreads out into a hollow cone inside the crystal, emerging as a hollow cylinder. The intensity distribution beyond the crystal is described using an adapted paraxial wave dispersion model. We show, experimentally and theoretically, how this results in a transition from conical diffraction for wavelengths at which the crystal is aligned to double refraction for misaligned wavelengths when using a white light source. The radius of the ring and location of the focal image plane (FIP) are also observed to have a wavelength dependency. The evolution of the conically diffracted beam beyond the FIP into the far field is studied and successfully described using a theoretical model.