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Radius of curvature sign convention for optical design. Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis. The vertex of the lens
The phoropter measurement is made at a common vertex distance of 12 mm from the eye. The equivalent prescription at the patient's cornea (say, for a contact lens) can be calculated as follows (this example assumes a negative cylinder sign convention): Power 1 is the spherical value, and power 2 is the steeper power of the astigmatic axis:
where S 1 is the distance from the object to the lens, θ 2 is the distance from the lens to the image, and f is the focal length of the lens. In the sign convention used here, the object and image distances are positive if the object and image are on opposite sides of the lens. [45]
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.
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 ...
For concave lenses, the focal point is on the back side of the lens, or the output side of the focal plane, and is negative in power. A lens with no optical power is called an optical window, having flat, parallel faces. The optical power directly relates to how large positive images will be magnified, and how small negative images will be ...
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 ...
Sign convention for Gaussian lens equation [25] Parameter Meaning + Sign − Sign s o: The distance between an object and a lens. Real object Virtual object s i: The distance between an image and a lens. Real image Virtual image f: The focal length of a lens. Conversing lens Diverging lens y o: The height of an object from the optical axis ...