Radian, definition

The lateral image resolution is defined by the ability of the imaging system to differentiate between two point objects separated by a small distance. The minimum distance at which the objects can be successfully differentiated is defined to be the resolution. The resolution for millimeter-wave imaging systems is limited by diffraction of the electromagnetic waves. Two objects can be resolved by an imaging system if the phase variation across the aperture differs by at least 2tt radians or one cycle [54], This definition leads to an angular resolution of... 

Name, Symbol radian, rad-(plane angle) Definition The radian is the plane angle between two radii of a circle which cuts off, on the circumference, an arc equal in length to the radius. 

N VT only if N is in radians per unit time a radian by definition is dimensionless... 

In defining the resolution using equation 23, one must note that in an annular chromatograph, the effluent streams are constrained to elute in 2tc radians. In our model we consider the range of 6 to be (0, < ) and therefore it was necessary to modify this definition of Rg for instances where the front of one peak containing smaller solutes overlaps the opposite front of another peak containing larger solutes. In each case, the resolution between peaks was calculated for the separation between the closest fronts. 

Fig. 1.4 Definition of the polar coordinates r, 9, f) for a point shown here in pink r is the radial coordinate and 9 and j are angular coordinates. 9 and j are measured in radians (rad). Cartesian axes (x, y and z) are also shown.

As previously stated, there are two units in this class the radian, symbol rad, the SI unit of the quantity plane angle and the steradian, symbol sr, the SI unit of the quantity solid angle. Definitions of these units are given in Appendix A. 

Appendix A. Definitions of the SI Base Units and the Radian and Steradian... 

The following definitions of the SI base units are taken from NIST SP 330 the definitions of the SI supplementary units, the radian and steradian, which are now interpreted as SI derived units (see Sec. 3), are those generally accepted and are the same as those given in ANSI/IEEE Std 268-1992. 

Equation (29.1) has two primary physical parameters, the reference wave obliquity angle (3 (measured in radians) and the control line length Rp (see definition sketch in Fig. 29.1). The former is the wave obliquity measured at the updrift... 

The value of n is the refractive index of the solvent at the frequency V. For molecules in solution or crystals we are usually interested in the rotation per molecule instead of per cm. Furthermore, optical rotations have traditionally been measured in degrees/decimeter instead of radians/cm. Introducing these new definitions we have... 

Figure A9.4a shows that for two points a small distance apart along the electron s path the change of velocity is related to the angular displacement 8

Figure A9.6 Geometry required to define a small volume element St in spherical polar coordinates according to the small changes Sr, SO and S. The sides of the small element shown can be found using the definition of radians as the ratio of the arc length subtended by the angle and the radius.

Figure A10.4 (a) The coordinate system and definition of an infinitesimal volume c/r for cylindrical polar coordinates, the factor u enters dx because of the definition of an arc length using angles measured in radians, (b) A slice through the H—H bond showing the charge density on a plane perpendicular to the H2 Cco axis, (c) The geometry used to obtain the distances r and /-j from each nuclear centre these are the varieJales used in the s-orbital basis functions, since they define the nuclear-electron separations.

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