Difference between revisions of Vertex distance
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→Calculation: add note that the equivalence is only for distant objects.
(→Calculation: still hadn't convinced myself with the wording) |
(→Calculation: add note that the equivalence is only for distant objects.) |
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<math>D_C=\frac{1}{\frac{1}{D}-x}</math>, | <math>D_C=\frac{1}{\frac{1}{D}-x}</math>, | ||
where <math>D_C</math> is the perceived diopter number, <math>D</math> is the diopter strength of your lenses and <math>x</math> is the vertex distance in meters. It is important to note here that this equation is sensitive to minus signs of your diopter strength. | where <math>D_C</math> is the perceived diopter number, <math>D</math> is the diopter strength of your lenses and <math>x</math> is the vertex distance in meters. (More generally, <math>x</math> is the distance the lens is being moved from its original position.) It is important to note here that this equation is sensitive to minus signs of your diopter strength and the direction of movement. | ||
Example for a vertex distance of 15mm (=0.015m): | Example for a vertex distance of 15mm (=0.015m): | ||
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<math>-4.0 dpt: D_C=\frac{1}{\frac{1}{-4.0}-0.015}=-3.774 dpt</math> | <math>-4.0 dpt: D_C=\frac{1}{\frac{1}{-4.0}-0.015}=-3.774 dpt</math> | ||
In the above example the -4.0 dpt glasses yield the same level of correction as -3.75 dpt contact lenses. It can be seen that vertex distance ''' | In the above example the -4.0 dpt glasses yield the same level of correction as -3.75 dpt contact lenses, for distant objects. It can be seen that vertex distance appears to '''increase''' the strength of [[plus Lenses]] and '''decrease''' the strength of [[minus lenses]]. The effect is noticeable above 4.0 dpt and is mostly negligible for [[low myopia]]. | ||
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where <math>f_C = \frac{1}{D_C}</math> and <math>f = \frac{1}{D}</math> | where <math>f_C = \frac{1}{D_C}</math> and <math>f = \frac{1}{D}</math> | ||
Conceptually, the location of the [[Optics_related_math# | Conceptually, the location of the [[Optics_related_math#The_thin_lens_equation|image]] is changed because the lens has moved relative to the eye. For a distant source object, the image is formed at the focus point of the lens, and so simply moves with the lens. | ||
* for a minus lens, moving the virtual image further from | * for a minus lens, moving the virtual image further from the eye is equivalent to using a weaker minus lens | ||
* for a plus lens, moving the (real) image towards the | * for a plus lens, moving the (real) image towards the eye (so that it is not as far beyond the retina) is equivalent to using a stronger plus lens. | ||
Note that the equivalence relationship holds ''only'' for distant source objects: the behaviour of glasses and contact lenses will be different for all closer objects, and the near point in particular will be different. | |||
==References== | ==References== | ||