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Numerical aperture definitionphysics

Jun 7, 2019 — If the FOV is 125m/1000m the difference in angle between triangle and a segment of a circle method is 4.7*10-3. If FOV is 140m/1000m the ...

The function of the ocular lens is twofold: it magnifies the image formed by the objective lens, and it allows the viewer to comfortably observe the magnified ...

Numerical apertureformula

Oct 31, 2024 — ... mirror at the standard 1x and the other at 10x magnification. However, the mirror's charging cable sticks awkwardly out from the side of the ...

Numerical apertureof objective lens

Choosing a home for your bird is crucial to ensure that it will have a happy life, as part of its happiness depends on the space it has to move around, so, as a general rule, you should multiply the size of your bird by 1.5 to obtain the minimum size of the cage.The Vision Cage Model S01 is ideal for canaries, budgies and small birds because of its size.Remember the importance of keeping the cage clean, and regularly changing the water and food.

This is an exact equation relating the NA to the f/#, but it is often convenient to have an approximation for this. When n = 1 (medium is air) and if we use a small angle approximation (sin α ≈ tan α) then:

Numerical aperture definitionin optical

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Adaptive Optics is another solution to atmospheric blurring. An Adaptive Optics system corrects the optical disturbances that light encounters as it traverses ...

Now that we have briefly explained what numerical aperture is, we can equate it to f/#. As explained here, f/# is also a measure of how much light can get through a lens. f/# of a simple lens is defined by the following equation, where f is the focal length of the lens and D is the diameter (or more specifically the entrance pupil diameter for more complex lens systems).

Numerical apertureof microscope

In order to equate NA and f/#, we can use simple geometric relationships. Figure 3.1 shows a simple lens focusing light rays (blue lines) from infinity to a point. This creates a cone of light that can be described by numerical aperture using the previous equation. The half angle, α, can now be defined by the following equation:

Numerical apertureunit

Below are three sets of lens specifications that would result in the desired system NA. There is an infinite number of specifications that will give the desired NA if one is allowed to change more than one spec.

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To determine whether lens specifications are compatible, we need to find the resulting numerical aperture from the other three specifications. To do this we will first need to use the equation below to relate the image height h, focal length f and the half field of view Θ. This equation can be derived using simple geometry using the relationships shown in the red triangle in figure 3.2.

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Numerical aperture (NA) refers to the cone of light that is made from a focusing lens and describes the light gathering capability of the lens (similar to f/# ). NA is defined by the following equation, where n is the index of refraction of the medium (often n=1 for air), and α is the half angle of the cone of light exiting the lens pupil.

Now we can find the focal length of the lens by assuming that the customer wants entrance pupil diameter to stay at the specified 20mm.

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Vision® bird homes have many revolutionary design features that set it apart from traditional bird cages. Most cages come with pull-out drawers that fail to do a good job at collecting bird waste and create maintenance headaches as a result. Vision®’s unique no-drawer design simplifies cage cleaning—simply detach the cage portion and empty the contents of the base into the waste bin. The result is less time-consuming, messy cleanups associated with bird keeping, leaving you more time to enjoy your pet. Vision®’s deep base can handle multiple types of litter, while raised ridges inside the base provide air circulation and help prevent mildew. The bird homes also allow non-invasive, exterior access to seed/water cups, reducing stress to birds during maintenance. In addition, multi-grip perches promote circulation and help prevent foot problems. The knock-down cages are easy to assemble.Includes: blue perches, blue food and water dishes.Vision® bird homes are available in a variety of sizes, as well as in small or large wire cage sizes. They are recommended for bird species as listed due to their natural behaviors and not by size of bird.The small cage is suitable for Budgies, Canaries, Lovebirds, and Finches.Horizontal wire: 1.6 mm (0.06")Vertical wire: 2.6 mm (0.10")Wire spacing (center to center): 12.3 mm (0.48")

Numerical apertureof lens

Numerical apertureof optical fiber

So what if the customer needs a numerical aperture of 0.25? To get this, at least one of the other specifications need to change. To do this, lets start with the initial specification for NA=0.25 and find what the f/# would be using this spec.

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Often times when starting the design process one can inadvertently request conflicting specifications. This example will show how easy this is to do and how to avoid it when specifying a lens.

If the medium is not air, as is common for some microscope objectives, the approximation above can be multiplied by the index of refraction of the medium as shown below.