Adolf attended the Potsdam Gymnasium and the Universities of Berlin and Göttingen. In 1889 he received his doctorate for a thesis on the actinometry of photographic astronomic fixed star exposures.
In 1887 Adolf promoted magnesium flashlight photography in Germany together with Johannes Gaedicke. Joining Dr. Hartnack's firm in Potsdam in 1889, he developed new microscope and photographic lenses. Later he developed a telephoto lens while working with Schulze & Bartels in Rathenow, from 1891 to 1894. Then Miethe joined Voigtländer &. Sohn as a research scientist, becoming one of its first directors upon its incorporation. The scientist took over as a professor of photochemistry at the Technische Hochschule in Berlin, Germany, in 1899. After Hermann Vogel died, and the department expanded under his direction to include photomechanical reproduction and spectrophotometry. Miethe directed the Photographisches Wochenblatt, from 1889. In 1894 founded Das Atelier des Photographen and Photographische Chronik, which he directed for the next twenty-five years. In 1904 he became head of the Technische Hochschule in Berlin.
Miethe helped pioneer the production of panchromatic emulsions for color photography by his discovery, with Arthur Traube in 1902, of ethyl red, the first color sensitizer of the isocyamne series. His final set of experiments, in 1926, explored the use of ultraviolet light in photographing fossils.