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Numerical aperture of a thin lens. Numerical aperture is not typically used in photography. Instead, the angular aperture of a lens (or an imaging mirror) is expressed by the f-number, written f /N, where N is the f-number given by the ratio of the focal length f to the diameter of the entrance pupil D: =.
where N is the uncorrected f-number, NA i is the image-space numerical aperture of the lens, | | is the absolute value of the lens's magnification for an object a particular distance away, and P is the pupil magnification. Since the pupil magnification is seldom known it is often assumed to be 1, which is the correct value for all symmetric lenses.
Aperture real amplitude as estimated at focus of a half inch perfect lens having Fresnel number equal to 0.01. Adopted wavelength for propagation is 1 μm. The Fresnel number is a useful concept in physical optics .
In a medium with an index of refraction close to 1, such as air, the angular aperture is approximately equal to twice the numerical aperture of the lens. [1] Formally, the numerical aperture in air is: = / = In the paraxial approximation, with a small aperture, <: /
Here NA is the numerical aperture, is half the included angle of the lens, which depends on the diameter of the lens and its focal length, is the refractive index of the medium between the lens and the specimen, and is the wavelength of light illuminating or emanating from (in the case of fluorescence microscopy) the sample.
As with objective lenses, a condenser lens with a maximum numerical aperture of greater than 0.95 is designed to be used under oil immersion (or, more rarely, under water immersion), with a layer of immersion oil placed in contact with both the slide/coverslip and the lens of the condenser. An oil immersion condenser may typically have NA of up ...
State of the art objectives can have a numerical aperture of up to 0.95. Because sin α 0 is always less than or equal to unity (the number "1"), the numerical aperture can never be greater than unity for an objective lens in air. If the space between the objective lens and the specimen is filled with oil however, the numerical aperture can ...
A more typical consumer zoom will have a variable maximum relative aperture since it is harder and more expensive to keep the maximum relative aperture proportional to the focal length at long focal lengths; f /3.5 to f /5.6 is an example of a common variable aperture range in a consumer zoom lens. By contrast, the minimum aperture does not ...