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In astronomy, the angular size or angle subtended by the image of a distant object is often only a few arcseconds (denoted by the symbol ″), so it is well suited to the small angle approximation. [7] The linear size (D) is related to the angular size (X) and the distance from the observer (d) by the simple formula:
Using a small-angle approximation, the angular resolution may be converted into a spatial resolution, Δℓ, by multiplication of the angle (in radians) with the distance to the object. For a microscope, that distance is close to the focal length f of the objective. For this case, the Rayleigh criterion reads:
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). [1] [2] A paraxial ray is a ray that makes a small angle (θ) to the optical axis of the system, and lies close to the axis throughout the system. [1]
Geometrical optics does not account for certain optical effects such as diffraction and interference, which are considered in physical optics. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts.
Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered. [1] In this approximation, trigonometric functions can be expressed as linear functions of the ...
an object of diameter 725.27 km at a distance of 1 astronomical unit (AU) an object of diameter 45 866 916 km at 1 light-year; an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Thus, the angular diameter of Earth's orbit around the Sun as viewed from a distance of 1 pc is 2″, as 1 AU is the mean radius of Earth's orbit.
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.
As long as the FOV is less than about 10 degrees or so, the following approximation formulas allow one to convert between linear and angular field of view. Let be the angular field of view in degrees. Let be the linear field of view in millimeters per meter. Then, using the small-angle approximation: