Difference between revisions of Optics related math

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===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 object distance, the contribution from the reciprocal becomes negligible.

Similarly, if the object is at the focus of the lens (<math>s=f</math>), the transmitted light is parallel - we say it "focuses at <math>s'=\infty</math>", which means it never comes together into a focus.

===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.

When the object is brought even closer to the lens (<math>s < f</math>) the emerging rays are now diverging. When substituted into the equation, <math>s' < 0</math>. This is interpreted as a '''virtual image''', ''behind'' the lens. This is the mode in which reading glasses (plus lenses) are used - the eye is able to focus on the virtual image which appears to be further away than the real source object.

A diverging lens behaves in a similar way, but for distant objects - the light rays incident from the source object are refracted outwards so that they are diverging even faster. Again, a virtual focus is said to form behind 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.

The corrective lens for [[myopia]] is a diverging lens. It works by forming a virtual image of distant objects, and it is this virtual image that the near-sighted eye is able to focus on.

===Diopters are inverse meters===

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 ===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 object distance, the contribution from the reciprocal becomes negligible.
+Similarly, if the object is at the focus of the lens (<math>s=f</math>), the transmitted light is parallel - we say it "focuses at <math>s'=\infty</math>", which means it never comes together into a focus.
 ===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.
+When the object is brought even closer to the lens (<math>s < f</math>) the emerging rays are now diverging. When substituted into the equation, <math>s' < 0</math>. This is interpreted as a '''virtual image''', ''behind'' the lens. This is the mode in which reading glasses (plus lenses) are used - the eye is able to focus on the virtual image which appears to be further away than the real source object.
+A diverging lens behaves in a similar way, but for distant objects - the light rays incident from the source object are refracted outwards so that they are diverging even faster. Again, a virtual focus is said to form behind 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.
+The corrective lens for [[myopia]] is a diverging lens. It works by forming a virtual image of distant objects, and it is this virtual image that the near-sighted eye is able to focus on.
 ===Diopters are inverse meters===