straightshooter wrote:bladeracer and JohnV
The comments about exit pupil size in relation to parallax might seem intuitive but they are wrong.
Look at the formula. It does not include in the calculation either exit pupil size or magnification.
A large exit pupil diameter allows a fair amount of lateral variation in eye positioning without vignetting which in itself leads to potential parallax error.
In the precision shooting world "mirage caps" are now making an appearance. Their main function is to reduce the depth of field of the scope and it would also appear, as the formula explains, that they provide a side benefit of reducing the extent of potential parallax error.
The calculation includes objective lens diameter, which dictates exit pupil diameter, regardless of magnification. Exit pupil is objective diameter divided by magnification. A 4x50 has EP of 12.5mm, a 4x32 has EP of 8mm. The larger objective thus gives you more room to move your eye around behind the exit pupil, thus more room to be offset from the centre of it. My 40x56 has an EP of 1.4mm, very difficult to move your eye at all and still see down the "tube" of light, thus very difficult to have any parallax error at all.
To use your formula ((radius of objective lens) x |(target distance)) - (scope parallax focus distance)| / ((2 x (scope parallax focus distance)):
I'm assuming that using the standard objective sizes which are given in millimeters that the answer is also in millimeters, regardless of your units of distance.
40mm objective at 100m with 100m parallax, then at 200m without changing the parallax.
((20) x |(100)) - (100)| / ((2 x (100))
1900/200=9.5mm at 100m
Could there really be 10mm offset at 100m just from parallax despite having the parallax set to the correct range? It seems unlikely to me. With a 40-power scope I would think 20mm of "float" around the target would be very obvious to me, so obvious that I would be looking to adjust the parallax.
((20) x |(200)) - (100)| / ((2 x (100))
3900/200=19.5mm at 200m
This is believable but seems less than I'd expect to see with the parallax set at half the target distance, I would expect to see a lot more "float" across the target than 40mm.
((28) x |(100)) - (100)| / ((2 x (100))
2700/200=13.5mm at 100m
((28) x |(200)) - (100)| / ((2 x (100))
5500/200=27.5mm at 200m