Difference between revisions of Diopters
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=== Thin lens equation === | === Thin lens equation === | ||
The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref> see derivations | The focal length of a lens is given by the lens manufacturer's equation. Assuming the lens is much thinner than the radius of curvature, so assuming the lens thickness is zero, we get a simplified version of the lens maker's equation. We can do a few more derivations, we arrive at the thin - lens equation: <ref>see derivations at https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_ - _Optics_and_Modern_Physics_(OpenStax )/02%3A_Geometric_Optics_and_Image_Formation/2.05%3A_Thin_Lenses </ref> <math>{1}\frac{1} d_o}+\frac{1}{d_i}=\frac{1}{f}</math> According to the fineness lens sign convention, * di is positive if it is a real image from the side opposite of the lens to the object, and it is negative if it is a virtual image on the same side of the lens as the object. * f is positive for a converging lens and negative for a diverging lens. This is also sometimes presented in the Newtonian form: <math> | ||
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This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is | This is the resulting equation at the beginning of the article. This also explains why focal power is increased for objects at closer distances: traditional optometry calls this "addition" for [[ presbyopia ]], although they generally use the minimum amount required for you to be able to see at 40cm with full distance correction using housing. For example, if you choose 80 cm as the working distance for your [[ differentials ]] (resulting in an "addition" of +1.25 dpt), and your blur horizon is 50 cm (resulting in -2 dpt ), the formula is | ||
< math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1 }{ - 50\ cm }=1.25\ dpt + \left( - 2\ dpt\right) = - 0.75\ dpt </math> | < math>\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{80\ cm}+\frac{1 }{ - 50\ cm }=1.25\ dpt + \left( - 2\ dpt\right) = - 0.75\ dpt </math> | ||
=== Cylinder === | === Cylinder === | ||