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Lorentz factor. where and v is the relative velocity between two inertial frames. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames. As the relative velocity approaches the speed of light, γ → ∞. Time dilation (different times t and t' at the same position x in same inertial frame)
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:
Consider a space ship traveling from Earth to the nearest star system: a distance d = 4 light years away, at a speed v = 0.8c (i.e., 80% of the speed of light). To make the numbers easy, the ship is assumed to attain full speed in a negligible time upon departure (even though it would actually take about 9 months accelerating at 1 g to get up ...
The distance formula is homogeneous in each variable, with d(λu, μv) = d(u, v) if λ and μ are non-zero scalars, so it does define a distance on the points of projective space. A notable property of the projective elliptic geometry is that for even dimensions, such as the plane, the geometry is non- orientable .
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek ...
The main benefit of using optical power rather than focal length is that the thin lens formula has the object distance, image distance, and focal length all as reciprocals. Additionally, when relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
A moiré pattern formed by two units of parallel lines, one unit rotated 5° clockwise relative to the other. The fine lines that make up the sky in this image create moiré patterns when shown at some resolutions for the same reason that photographs of televisions exhibit moiré patterns: the lines are not absolutely level. Difference in ...