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Note however that in areas of optics other than design, other sign conventions are sometimes used. In particular, many undergraduate physics textbooks use the Gaussian sign convention in which convex surfaces of lenses are always positive. [3] Care should be taken when using formulas taken from different sources.
The sign of the weight of a tensor density, such as the weight of the determinant of the covariant metric tensor. The active and passive sign convention of current, voltage and power in electrical engineering. A sign convention used for curved mirrors assigns a positive focal length to concave mirrors and a negative focal length to convex mirrors.
When measuring the height of an inverted image using the cartesian sign convention (where the x-axis is the optical axis) the value for h i will be negative, and as a result M will also be negative. However, the traditional sign convention used in photography is "real is positive, virtual is negative". [1]
The cardinal points were all included in a single diagram as early as 1864 (Donders), with the object in air and the image in a different medium. Cardinal point diagram for an optical system with different media on each side. F for Focal point, P for Principal point, NP for Nodal Point, and efl for effective focal length. The chief ray is shown ...
A lens may be considered a thin lens if its thickness is much less than the radii of curvature of its surfaces (d ≪ | R 1 | and d ≪ | R 2 |).. In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces.
Similarly to curved mirrors, thin lenses follow a simple equation that determines the location of the images given a particular focal length and object distance (): + = where is the distance associated with the image and is considered by convention to be negative if on the same side of the lens as the object and positive if on the opposite side ...
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
A lens with a different shape forms the answer to Mrs. Miniver's problem, on finding a lens with half the area of the union of the two circles. Lenses are used to define beta skeletons, geometric graphs defined on a set of points by connecting pairs of points by an edge whenever a lens determined by the two points is empty.