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The numerical aperture with respect to a point P depends on the half-angle, θ1, of the maximum cone of light that can enter or exit the lens and the ambient index of refraction. As a pencil of light goes through a flat plane of glass, its half-angle changes to θ2. Due to Snell's law, the numerical aperture remains the same: NA = n1sin θ1 ...
f-number. Diagram of decreasing apertures, that is, increasing f-numbers, in one-stop increments; each aperture has half the light-gathering area of the previous one. An f-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is calculated by dividing the system's focal length by the diameter of the ...
The magnification of the eyepiece depends upon its focal length and is calculated by the same equation as that of a magnifying glass (above). Note that both astronomical telescopes as well as simple microscopes produce an inverted image, thus the equation for the magnification of a telescope or microscope is often given with a minus sign .
Focal length. The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror. The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a ...
Aperture. In biology, the pupil (appearing as a black hole) of the eye is its aperture and the iris is its diaphragm. In humans, the pupil can constrict to as small as 2 mm (f/ 8.3) and dilate to larger than 8 mm (f/ 2.1) in some individuals. In optics, the aperture of an optical system (including a system consisted of a single lens) is a hole ...
This magnification formula provides two easy ways to distinguish converging (f > 0) and diverging (f < 0) lenses: For an object very close to the lens (0 < S 1 < | f |), a converging lens would form a magnified (bigger) virtual image, whereas a diverging lens would form a demagnified (smaller) image; For an object very far from the lens (S 1 ...
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...
Defining equation SI units Dimension Lens power P = / m −1 = D (dioptre) [L] −1: Lateral magnification m = / = / dimensionless dimensionless Angular magnification m = / dimensionless dimensionless