This paper proposes a new and fundamental interpretation of the wave-particle duality of light based on the orthonormal basis in Hilbert space and Weyl's law. In this framework, the particle nature of light originates from individual orthonormal basis vectors, which are discrete, independent, and countable quantum units. The wave nature arises from the linear superposition, coherent transition, and temporal evolution of excitations among these orthogonal basis vectors. Weyl's law is used to rigorously count the total number of independent basis states, avoiding classical assumptions and phase-space approximations. The wave-particle duality is therefore not a complementary phenomenon, but two distinct manifestations of the same set of orthogonal basis systems: particle behavior corresponds to the existence of a single basis, while wave behavior corresponds to the coherent superposition and propagation among multiple bases.