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Normal optical microscopes can magnify up to 1500× with a theoretical resolution of 0.2 μm . The lenses can be quite complicated and are composed of multiple elements to reduce aberrations. Microscope objective lenses are particularly important as they primarily gather light from the specimen. Three parameters describe microscope objectives: the numerical aperture (NA) , the magnification ( m ) size 12{ \( m \) } {} , and the working distance. The NA is related to the light gathering ability of a lens and is obtained using the angle of acceptance θ size 12{θ} {} formed by the maximum cone of rays focusing on the specimen (see [link] (a)) and is given by

NA = n sin α, size 12{ ital "NA"=n"sin"α} {}

where n size 12{n} {} is the refractive index of the medium between the lens and the specimen and α = θ / 2 size 12{α= {θ} slash {2} } {} . As the angle of acceptance given by θ size 12{θ} {} increases, NA becomes larger and more light is gathered from a smaller focal region giving higher resolution. A 0 . 75 NA size 12{0 "." "75" ital "NA"} {} objective gives more detail than a 0 . 10 NA size 12{0 "." "10" ital "NA"} {} objective.

Part a of the figure shows a horizontal dotted line, a point P on the line and an objective lens at a distance from the point such that a triangle is formed from point P to the edges of the lens. An angle theta is shown at point P, representing the maximum cone of rays entering the lens from point P. Part b of the figure shows light rays from a specimen entering a camera lens held above it. The rays form an inverted cone.
(a) The numerical aperture (NA) of a microscope objective lens refers to the light-gathering ability of the lens and is calculated using half the angle of acceptance θ . (b) Here, α is half the acceptance angle for light rays from a specimen entering a camera lens, and D is the diameter of the aperture that controls the light entering the lens.

While the numerical aperture can be used to compare resolutions of various objectives, it does not indicate how far the lens could be from the specimen. This is specified by the “working distance,” which is the distance (in mm usually) from the front lens element of the objective to the specimen, or cover glass. The higher the NA size 12{ ital "NA"} {} the closer the lens will be to the specimen and the more chances there are of breaking the cover slip and damaging both the specimen and the lens. The focal length of an objective lens is different than the working distance. This is because objective lenses are made of a combination of lenses and the focal length is measured from inside the barrel. The working distance is a parameter that microscopists can use more readily as it is measured from the outermost lens. The working distance decreases as the NA size 12{ ital "NA"} {} and magnification both increase.

The term f / # size 12{ {f} slash {#} } {} in general is called the f size 12{f} {} -number and is used to denote the light per unit area reaching the image plane. In photography, an image of an object at infinity is formed at the focal point and the f size 12{f} {} -number is given by the ratio of the focal length f size 12{f} {} of the lens and the diameter D size 12{D} {} of the aperture controlling the light into the lens (see [link] (b)). If the acceptance angle is small the NA size 12{ ital "NA"} {} of the lens can also be used as given below.

f /# = f D 1 2 NA . size 12{f"/#"= { {f} over {D} } approx { {1} over {2 ital "NA"} } } {}

As the f size 12{f} {} -number decreases, the camera is able to gather light from a larger angle, giving wide-angle photography. As usual there is a trade-off. A greater f / # size 12{ {f} slash {#} } {} means less light reaches the image plane. A setting of f / 16 size 12{ {f} slash {"16"} } {} usually allows one to take pictures in bright sunlight as the aperture diameter is small. In optical fibers, light needs to be focused into the fiber. [link] shows the angle used in calculating the NA size 12{ ital "NA"} {} of an optical fiber.

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
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s.
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Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
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s.
Graphene has a hexagonal structure
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
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AMJAD
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Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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Source:  OpenStax, Physics for the modern world. OpenStax CNX. Sep 16, 2015 Download for free at http://legacy.cnx.org/content/col11865/1.3
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