Answers to questions on prism offsets.

Figure 1.
Q: Why are there so many types of prisms with different offsets? Now that zero offsets are common, why even have the others?

A: For a lot of prisms, the “traditional” offset has been –30 mm. More than likely this number came about because it was a good compromise when considering how to mount the prism over the plumb line (of the prism pole or tribrachs) for balance and compactness. Without considering that the medium is glass in a prism, the length of the EDM’s light path through the prism is easy to compute (see Figure 1).

Figure 2.
However, physics tells us that because they are glass, peculiarity of retroprisms is that the EDM “thinks” that the back corner of the prism is further back than it physically is because light slows down when it enters the prism (see Figure 2). Glass has a higher index of refraction than air, so the EDM “thinks” that the light path within the prism is longer than it really is because the assumption is that the light is traveling only through air. However, when measuring angles, if the center of the prism is sighted, rather than a target that is aligned with the plumb line, the apparent position of the center is closer than it really is. This is readily observed when looking down at a fish in an aquarium through the top and then looking in from the side when it appears to be much closer.

It is this latter phenomenon that causes problems when zero offset prisms are used. To make zero offset prisms possible, the prisms must be cantilevered well out in front of the plumb line. This projects the apparent center of the prism even further away from the plumb line. If no target is used and there is any error, horizontally or vertically in pointing the prism at the instrument, a displacement will occur in the apparent prism center, resulting in horizontal and/or vertical angle error.

It is for this reason that prisms with apparent centers that are as nearly as possible coincident with the location of the plumb line are produced. So-called 30 mm prisms (actually –30 mm) and 40 mm prisms have been used when these kinds of targeting errors need to be minimized. If a zero offset prism is not accurately pointed back at the instrument, angle errors will result if no target or an improper target assembly is used with the prism. Inaccurate pointing of the prism can also result in distance errors. The surveyor, as expert measurer, should select prisms that are consistent with instrument capabilities, field processes and survey requirements.

Have a question for the GIAA Mailbag? Please E-mail your questions to Diana Brown at brownd@bnp.com. Your questions, and their responses from qualified professionals, will help others. You may also ask your questions or continue the discussion at www.rpls.com.

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