Zinc oxide (ZnO) micro and nanostructures were synthesised on a quartz substrate by the carbothermal evaporation method. The thin layers of gold were used as a catalyst and syntheses were carried out at different persistence time. Characterisation of the layer was conducted in order to study the effect of persistence time on morphology and crystal structure and optical properties of the fabricated ZnO nanostructures. The samples were characterised by scanning electron microscopy, X-ray diffraction (XRD) and UV–vis spectrophotometry which were performed to investigate the optical properties of the fabricated ZnO layer. The XRD spectrum clearly shows that the structure is in a hexagonal wurtzite phase. Optical properties of ZnO micro and nanostructures were evaluated from transmittance data using the method proposed by Swanepoel (in the regions λ = 200–900 nm). The study’s results indicate that increasing the persistence time as well as decreasing the size of ZnO nanostructures enhances the optical bandgap to about 3.‏46 eV. To the best of this work's knowledge, this is the first report on the study of the correlation of optical properties obtained by Swanepoel method and morphology of ZnO nanostructures.