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Numerical aperture meaningin physics

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Numerical apertureof objective lens

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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.

Numerical aperture meaningin optical

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Our current use of rare earth metals has huge implications in terms of toxic pollution. They are often mined using extremely energy-intensive processes, spewing carbon emissions into the atmosphere and toxins into the ground. Indeed, the metals involved, which include mercury, barium, lead, chromium and cadmium, are extremely damaging to the environment. Recent survey findings from United Nations University (UNU) and the World Health Organisation (WHO) on the impact e-waste has on child health, raised concerns around chemical burns, cancer and stunted growth. Eradicating these substances from discarded products is difficult and costly, which is why much of the e-waste exported to the developing world under the pretence of being reused or refurbished ends up being dumped. The WHO has reported that 23% of deaths in the developing world are attributable to environmental factors, one of which is pollution, and that environmental risk factors contribute to more than 80% of regularly reported diseases.

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:

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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:

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With rare earth metals becoming increasingly scarce and China tightening its grip on the mining industry, tech manufacturers and consumers need to rethink how they market and consume technology. Companies must refrain from tearing out IT infrastructure unless it is absolutely necessary, while manufacturers must take a much more responsible approach to their production processes. As consumers, we must break the upgrade habit and keep devices for longer, considering repair before replacement. And we mustn't forget that when technology does eventually come to the end of its lifecycle, it must be disposed of both safely and ethically.

Numerical apertureof microscope

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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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Rare earth metals are the crucial ingredient in many of our tech products. From smartphones, tablets and laptops, to the niche technology used by the military and medical profession, all depend on them to function, for features as broad as a phone's coloured screen to the magnets used to power hybrid cars. As new technology continues to flood the market, the demand for these metals will grow, but they're already in short supply.

Recycling rare earth materials is particularly challenging as, once embedded in devices, they're difficult to take out. Instead of discarding phones or IT equipment after a couple of years, enterprises should aim to get the most out of technology they have invested in through repairing or refurbishing.

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.

If we're going to ensure that there are enough rare earth metals to keep pace with the current rate of technological innovation, and if we're going to stop these dangerous metals from filling landfill sites, we need to end today's rip-and-replace attitude towards IT equipment, as well as an end to the overproduction of devices by manufacturers.

Numerical apertureof lens

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).

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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.

Another byproduct of innovation is that countless products never get used at all. Inflexible production processes, such as with mass production lines, where it is difficult to alter the design of a product or allow variation in the process sequences, means that the tech industry can be guilty of producing more equipment than the market actually wants or that doesn't fit exactly what the market needs. This renders stacks of brand new phones, tablets and set top boxes obsolete, left to gather dust in warehouses.

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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.

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.

With the sheer number of new gadgets and business solutions coming onto the market every year, it's no surprise that rare earth metals are becoming scarce. However, the likelihood of a shortage is increased by the lack of mining that's taking place outside China. China has the lion's share of these precious metals but has been reluctant to export them to other countries in an effort – it says – to conserve its own resources. In recent years, it has cut its exports by more than 70%, severely impacting manufacturing in countries such as Japan and the US, while enabling manufacturing in China itself. In addition to these trade restrictions, China is using its economic clout to undercut the prices offered by mines in other regions, effectively forcing them out of business.

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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.

By actively creating today's upgrade mentality, where customers are encouraged to replace perfectly good IT solutions or devices with new technology, manufacturers are ensuring that too many rare earth metals end up in the tip. This situation is made worse by the fact that manufacturers are often quick to withdraw support for their older products lines. Apple, for example, withdraws support for products which have been discontinued for more than seven years; after this, customers receive no service and spare parts are no longer available. With no reassurance that their infrastructure can be serviced or repaired, companies are forced to discard older equipment, regardless of its condition.