Difference between revisions of Diopters
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{{ See also |Astigmatism#Spherical equivalent }} | {{ See also |Astigmatism#Spherical equivalent }} | ||
Calculating the average value over all angles using an integral, the result <ref> | Calculating the average value over all angles using an integral, the result <ref>Just integrate one or two periods: https://www.wolframalpha.com/input/?i=average+de+%28sin+x%29%5E2+de+0+à+2+pi</ref> is | ||
<math>P_{avg} = \lim_{T \to \infty} \frac{ 1}{2T} \int_{ - T}^{T} P_{cyl} (\sin{t})^2 \,dt = \frac{1}{2} P_{cyl}</math> | <math>P_{\text{avg}} = \lim_{T \to \infty} \frac{ 1}{2T} \int_{ - T}^{T} P_{\text{cyl}} (\sin{t})^2 \,dt = \frac{1}{2} P_{\text{cyl}}</math> | ||
C' is why the spherical equivalent has power equal to half the power of the cylinder. | C' is why the spherical equivalent has power equal to half the power of the cylinder. | ||
==== Adding/Combining Lenses ==== | ==== Adding/Combining Lenses ==== | ||