In this work, we employ first-principles calculations to investigate the optical properties of boron nitride nanoribbons with reconstructed edges. We found that because of the presence of homopolar B-B and N-N bonds in the edges, such nanoribbons, unlike boron nitride nanotubes, absorb light and have non-null optical conductivity in the visible and infrared range. The stoichiometry and distribution of the homopolar bonds in the edges change the absorption, reflectance, refraction index, and optical conductivity of nanoribbons, which may allow the tuning of those properties. Regarding the absorption in the infrared and visible range, the nanoribbons with B excess are almost unaffected by the direction of light incidence. On the other hand, the direction of light incidence strongly affects the intensity of the absorption peaks of nanoribbons with N excess in the region. At ultraviolet and above non-cylindrical geometry of the ribbons with the homopolar bonds at the edges also lead to a dependence of the optical properties with the direction of light incidence.