We demonstrate that the interhand dielectric function and its k-th derivative spectrum near an n-dimensional critical point can be evaluated from the harmonic oscillator dielectric function and its k-th derivative spectrum, respectively, by using n/2-fold integration. The physical characteristics of harmonic oscillator in the interband spectra of an n-dimensional solid are exhibited by the action of n/2-fold integral operator. Relations between interband transitions and harmonic oscillator model, and between optical properties and dimensionality are discussed. In the fractional integral expressions for the interband optical responses, dimensionality n can be generated to an arbitrary continuous parameter.