This talk explores the concentration of transmission eigenfunctions near the boundary of disks and balls with a positive constant refractive index different from one. We present explicit lower and upper bounds for the spectral density of surface-localized eigenmodes in acoustic scattering. The analysis combines Bessel function estimates with eigenvalue counting arguments. We also discuss corresponding results for Maxwell’s equations, including both transverse electric and transverse magnetic modes. These results provide a quantitative understanding of how frequently boundary localization occurs in transmission eigenvalue problems.