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The signs are reversed for the back surface of the lens: R 2 is positive if the surface is concave, and negative if it is convex. This is an arbitrary sign convention; some authors choose different signs for the radii, which changes the equation for the focal length. For a thin lens, d is much smaller than one of the radii of curvature (either ...
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.
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]
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 ...
Image distance in a spherical mirror + = () Subscripts 1 and 2 refer to initial and final optical media respectively. These ratios are sometimes also used, following simply from other definitions of refractive index, wave phase velocity, and the luminal speed equation:
The image recorded by a photographic film or image sensor is always a real image and is usually inverted. 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.
The total aberration of two or more very thin lenses in contact, being the sum of the individual aberrations, can be zero. This is also possible if the lenses have the same algebraic sign. Of thin positive lenses with n=1.5, four are necessary to correct spherical aberration of the third order.
To focus light to the same image location: = where f c is the corrected focal length for the new lens, f is the focal length of the original lens, and x is the distance that the lens was moved. The value for x can be positive or negative depending on the sign convention. Lens power in diopters is the mathematical inverse of focal length in meters.