Difference between revisions of Diopters
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==== Spherical Equivalent ==== | ==== Spherical Equivalent ==== | ||
By calculating the average value over all angles using an integral, the result is | By calculating the average value over all angles using an integral, the result<ref>it is only necessary to integrate one or two periods: https://www.wolframalpha.com/input/?i=average+of+%28sin+x%29%5E2+from+0+to+2+pi</ref> is | ||
<math>F_{avg} = \frac{1}{2} F_{cyl}</math> | <math>F_{avg} = \lim_{T \to \infty} \frac{1}{2T} \int_{-T}^{T} F_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} F_{cyl}</math> | ||
This is why the spherical equivalent has power equal to half of the cylinder's power. | This is why the spherical equivalent has power equal to half of the cylinder's power. | ||