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Prentice's rule
We know Prentice's rule, power times decentration, in centimeters. What about a vertical component in compound prism initiated by horizontal decentration of an oblique axis spherocylinder? Essentially, this prism is manifest without any decentration in the direction of the base or apex orientation, which, in my mind, is contrary to Prentice's rule. This just occured to me out of the blue. Am I missing something?
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The short answer is that Prentice's rule is still valid in your example. When you decenter an oblique cylinder, the original point is actually left at both a vertical and a horizontal separation when measured perpendicular to the planes containing the principal meridians of the lens. If I have time later, I'll try to draw you an example to illustrate this effect.