Optical Rangefinders, Bigger is More Accurate

 Last time we touched on the fact that bigger is better when it comes to using a rangefinder to measure extremely long distances.   Today we’ll expand on that theme and discover how bigger is indeed more accurate.       Returning to our previous example, we’re still trying to find the distance to that ship on the horizon.   We’ve got two rangefinders at our disposal, one short, one long, and the measurements provided by them are vastly different.   Which is correct?   To find out, we’ll hypothesize that we’ve taken the time to meticulously measure the distance the hard way, with a really long tape measure.   Doing so, we find the actual distance to the ship is 5280 feet.       We can now compare the actual measured distance to the measurements taken with our two rangefinders and compare their accuracy: Rangefinder One = 5729 feet – 5280 feet = 449 feet Rangefinder Two = 5208 feet – 5280 feet = -72 feet       The smaller rangefinder results in a difference, or error, of 449 feet, while the bigger results in a difference of 72 feet.   It’s clear that the bigger rangefinder gets us closer to the actual measurement taken by tape measure, so it’s the most accurate.       The obvious conclusion is that the bigger the rangefinder used, the smaller the error factor.  That’s because as the length of the rangefinder increases, the smaller the angle θ becomes, a situation which results in the tangent of θ moving farther away from rather than closer to 90°, all of which translates to more accuracy in our rangefinder’s measurements.  Put another way, the bigger the rangefinder, the less likelihood there is of its angle θ‘s tangent hovering near 90° and becoming asymptotic, an undesirable outcome for reasons explained in a previous blog in this series.       Next time we’ll see how early astronomers were able to arrive at relatively accurate calculations of the distances between Earth and other heavenly bodies by using the parallax effect produced by the world’s largest optical rangefinder, Planet Earth itself. ____________________________________