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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.
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:
This is any lens with a focal length longer than the diagonal measure of the film or sensor. [121] The most common type of long focus lens is the telephoto lens, a design that uses a special telephoto group to be physically shorter than its focal length. [122] Modern zoom lenses may have some or all of these attributes.
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 ...
With vision in fish and amphibians, the lens is fixed in shape, and focusing is instead achieved by moving the lens forwards or backwards within the eye using a muscle called the retractor lentus. [54] In cartilaginous fish, the suspensory ligaments are replaced by a membrane, including a small muscle at the underside of the lens. This muscle ...
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The bottom example depicts a real lens with spherical surfaces, which produces spherical aberration: The different rays do not meet after the lens in one focal point. The further the rays are from the optical axis, the closer to the lens they intersect the optical axis (positive spherical aberration). (Drawing is exaggerated.)