The optical properties of BAlN and BGaN ternary alloys are investigated using first-principle calculation. Hybrid density functional theory is applied to determine the refractive indices of different alloys. A peculiar non-linear behavior of the static refractive index as a function of boron composition is found. The results of this calculation are interpolated to generate a three dimensional dataset, which could be used for designing a myriad of strained and strain-free optoelectronic and photonic devices. This is then used to find a lattice-matched heterostructure optimized for DBR applications (B0.108Ga0.892N/AlN). A DBR design with 25 pairs at a wavelength of 375 nm is found to have peak reflectivity of 99.8% and a bandwidth of 26 nm.