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The principle of the optical rangefinder is rather simple; from where you are look straight ahead. In the center of your field of view there will be something, for example a doorhandle. Now, while looking straight ahead, move sidewise one meter. You will notice that the doorhandle is no longer in the center of your field of view; it will now be at an angle. That angle depends directly from your distance to the doorhandle. This simple principle is embodied in a instrument of great elegance, able to measure distances from some centimeters up to tens of kilometers

This is the scheme:

 | \
 |  \
 |   \ 
 |    \
 |     \
 |      \ 
 |       \
 |        \
 |         \
 |          \
 |           \
 |            \
 |             \
 |              \
 |right angle    \
 \----------------\ Mobile mirror at angle alpha
Fixed mirror      |     
                  O eyepiece

the observer's eye placed in O will see two images of A, one coming from the fixed mirror, the other from the mobile mirror. The observer will rotate the mobile mirror M until the two images of A overlap. At that point the triangle AFM will have one straight angle in F, one known angle in M, and one known side FM (known as the base length). At that point the unknown segment AF can be computed by solving this:

AF = FM * tan(alfa)

The solution (also known as the range) can be obtained directly by mechanical means applied to the gear that rotates M. Trig tells us that the error increases with the distance; as the distance gets greater, we are required to measure with increasing precision angles that get closer and closer to a right angle.

Optical rangefinders are used in rangefinder cameras, and artillery. In the first application, precision is important only at small ranges; the behaviour of depth of field will quickly shadow errors for distances beyond the tenths of meters - this is why one can get away with a base length of some centimeters and magnifications of less than 1 - that's to say, optical systems that actually reduce rather than magnify.

For artillery applications, quite the opposite holds; accuracy is increased by having a large base length and using magnification on both mirrors (on warships of the Iowa class the base length is around 8 meters, and the magnification is 25x). Under these conditions, the accuracy is of a couple of meters at 2000 meters of range, and around 10 meters at 20 kilometers. Of course, operator accuracy becomes the limiting factor when the platform for all this trigonometry is a warship travelling at 30 knots on Atlantic swells and occasionally shooting shells that weigh more than a car.

For fascinating details, please read http://www.warships1.com/W-Tech/tech-078.htm

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