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In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...
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:
Most curved mirrors have a spherical profile. [7] These are the simplest to make, and it is the best shape for general-purpose use. Spherical mirrors, however, suffer from spherical aberration—parallel rays reflected from such mirrors do not focus to a single point.
In particular, spherical mirrors exhibit spherical aberration. Curved mirrors can form images with magnification greater than or less than one, and the image can be upright or inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen. [3]
The optical center of a spherical lens is a point such that if a ray passes through it, the ray's path after leaving the lens will be parallel to its path before it entered. In the figure at right, [ 8 ] the points A and B are where parallel lines of radii of curvature R 1 and R 2 meet the lens surfaces.
Instead, the angular aperture of a lens (or an imaging mirror) is expressed by the f-number, written f /N, where N is the f-number given by the ratio of the focal length f to the diameter of the entrance pupil D:
Stepwise magnification by 6% per frame into a 39-megapixel image. In the final frame, at about 170x, an image of a bystander is seen reflected in the man's cornea. Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification.
A spherical Fresnel lens is equivalent to a simple spherical lens, using ring-shaped segments that are each a portion of a sphere, that all focus light on a single point. This type of lens produces a sharp image, although not quite as clear as the equivalent simple spherical lens due to diffraction at the edges of the ridges.