Difference between revisions of Optics related math
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separate out thin lens equation as a separate section, and flesh it out slightly.
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(separate out thin lens equation as a separate section, and flesh it out slightly.) |
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==Diopters are inverse meters== | ==The thin lens equation== | ||
<math>\frac{1}{f} = (\frac{1}{s}) + (\frac{1}{s'})</math> | |||
where | |||
* <math>f</math> = focal length of lens | |||
* <math>s</math> = distance to object | |||
* <math>s'</math> = distance to image | |||
===Infinity=== | |||
The term '''object at infinity''' is often used. When <math>s=\infty</math> is substituted into the thin lens equation, that term vanishes, so that the focal length is then just the image location. For any sufficiently large image distance, the contribution from the reciprocal becomes negligible. | |||
===Virtual image=== | |||
A converging lens (such as a magnifying glass) behaves like a "typical" lens - the incoming light is brought to a focus on the opposite side of the lens. | |||
A diverging lens behaves differently - the light rays spreading from the source object are refracted outwards so that they are diverging even faster. They are not brought to a focus in any intuitive sense. Instead, the light behaves ''as if'' it was coming from a closer object. This is termed a '''virtual''' image - it lies between the source object and the lens. The thin lens equation still works as long as you use negative numbers to describe both the (virtual) image location and the focal length. | |||
The corrective lens for [[myopia]] is a diverging lens. It works by forming a virtual image of objects far away, and it is that virtual image that the near-sighted eye is able to focus on. | |||
===Diopters are inverse meters=== | |||
Intuitively, the more powerful a lens is, the more rapidly it can bring incoming light to a focus. So the power is defined as the inverse of the focal length. | |||
''See Also [[Diopters]]'' | ''See Also [[Diopters]]'' | ||
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{{#ev:youtube|9z2jjT_Gm7o|400}} | {{#ev:youtube|9z2jjT_Gm7o|400}} | ||
==Visual acuity equation== | ==Visual acuity equation== | ||