Search results
Results from the WOW.Com Content Network
Similarly, f is strictly logarithmically convex if and only if, in the above two expressions, strict inequality holds for all t ∈ (0, 1). The above definition permits f to be zero, but if f is logarithmically convex and vanishes anywhere in X, then it vanishes everywhere in the interior of X.
A convex mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc. A convex mirror or diverging mirror is a curved mirror in which the reflective surface bulges towards the light source. [1] Convex mirrors reflect light outwards, therefore they are not used to focus light.
Every concave function that is nonnegative on its domain is log-concave. However, the reverse does not necessarily hold. An example is the Gaussian function f(x) = exp(−x 2 /2) which is log-concave since log f(x) = −x 2 /2 is a concave function of x. But f is not concave since the second derivative is positive for | x | > 1:
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
The focal point F and focal length f of a positive (convex) lens, a negative (concave) lens, a concave mirror, and a convex mirror. The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power.
A log–log plot of y = x (blue), y = x 2 (green), and y = x 3 (red). Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right).
In other words, a real image is an image which is located in the plane of convergence for the light rays that originate from a given object. Examples of real images include the image produced on a detector in the rear of a camera, and the image produced on an eyeball retina (the camera and eye focus light through an internal convex lens).
A convex secondary mirror is placed just to the side of the light entering the telescope, and positioned afocally so as to send parallel light on to the tertiary. The concave tertiary mirror is positioned exactly twice as far to the side of the entering beam as was the convex secondary, and its own radius of curvature distant from the secondary.