What is the difference between ¼ wave, 1/10 wave, and 1/20 wave mirrors?

These values refer to the surface accuracy specification for the polished substrate of a mirror. Surface Accuracy describes the maximum allowable deviation of an optical surface from a perfect surface. If the mirror were flat, the value would give a reference as to "how flat". Since the test method used for inspecting surface accuracy uses a specific wavelength, the value is defined in terms of this wavelength. All catalog values refer to a maximum peak-to-valley value at 632.8nm. For high accuracy parts, the amount of deviation is so small that the value is defined as a fraction of a wavelength of light. For example, a ¼-wave mirror has a surface accuracy of 158.2nm (0.25 x 632.8nm), which is equivalent to 6.2 micro inches. The lower the value of the fraction, the higher the accuracy. Typically only values less than ¼-wave are considered as precision and values less than 1/10-wave as high precision quality. As a comment on notation, the following values are equivalent: ¼-wave, ¼λ, and λ/4, where λ is the value of the test wavelength.