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Due to Snell's law, the numerical aperture remains the same: NA = n 1 sin θ 1 = n 2 sin θ 2. In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
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. The Fresnel number establishes a coarse criterion to define the near and far field approximations.
Memorial in Jena, Germany to Ernst Karl Abbe, who approximated the diffraction limit of a microscope as = , where d is the resolvable feature size, λ is the wavelength of light, n is the index of refraction of the medium being imaged in, and θ (depicted as α in the inscription) is the half-angle subtended by the optical objective lens (representing the numerical aperture).
The f-number (also called the ' relative aperture '), N, is defined by N = f / E N, where f is the focal length and E N is the diameter of the entrance pupil. [2] Increasing the focal length of a lens (i.e., zooming in) will usually cause the f-number to increase, and the entrance pupil location to move further back along the optical axis.
Viewing the aperture of radius d/2 and lens as a camera (see diagram above) projecting an image onto a focal plane at distance f, the numerical aperture A is related to the commonly-cited f-number N= f/d (ratio of the focal length to the lens diameter) according to
The numerical aperture of a Gaussian beam is defined to be NA = n sin θ, where n is the index of refraction of the medium through which the beam propagates. This means that the Rayleigh range is related to the numerical aperture by z R = n w 0 N A . {\displaystyle z_{\mathrm {R} }={\frac {nw_{0}}{\mathrm {NA} }}.}
Rudolf Kingslake (1951) Lenses in Photography defines f-number and effective f-number like I do "effective f-number of a lens is equal to its true f-number multiplied by (1+)" (p.99), but on p.98 defines f-number both as focal length over aperture diameter and as 1/2sin(theta'); he has a footnote about how the second principal plane is actually ...