Vertical Asymptotes and Optical Distance Measurement

      Last time we introduced the vertical asymptote and the fact that it’s associated with the tangent function when angles approach 90° in value.   On a graph that looks like this:

mechanical engineering expert witness

Figure 1

      This asymptotic relationship exists when attempting to use an optical rangefinder to determine the distance to objects that are extremely far away– as in so far away they can barely be seen by the naked eye.   When this is the case, is it even possible to use the optical rangefinder?   Theoretically, yes.   But not without complications.

      Our attempt to use the rangefinder to do this is illustrated in Figure 2.

engineering expert witness

Figure 2

      You’ll note that the lines of sight extending from mirrors A and B on our rangefinder are almost parallel to each other, creating a situation where a vertical asymptote will form with regard to θ’s tangent.   In plain English this means that even minute changes in θ will result in huge changes to tan(θ).

      We’ll explore that subject next time.


Tags: , , , , , , ,

Comments are closed.