Lapping can be used to obtain a specific surface roughness; it is also used to obtain very accurate surfaces, usually very flat surfaces. Surface roughness and surface flatness are two quite different concepts. Unfortunately, they are concepts that are often confused by the novice.
A typical range of surface roughness that can be obtained without resort to special equipment would fall in the range of 1 to 30 Ra (average roughness in micrometers or microinches).
Surface accuracy or flatness is usually measured in Helium Light Bands, one HLB measuring about 0.000011 inches (11 millionths of an inch). Again, without resort to special equipment accuracies of 1 to 3 HLB are typical. Though flatness is the most common goal of lapping, the process is also used to obtain other configurations such as a concave or convex surface.
As a side note: Two parts that are lapped to a flatness of about 1HLB will exhibit "Wringing-in" or "Jo Blocking." A phenomenon where the two parts will cling to each other when placed in contact. The name "Jo-blocking" comes from the fact that gage blocks - sometimes called "Johansson blocks" after the manufacturer - can be made to stick together in this manner.
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