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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:
Angles involved in a thin gravitational lens system. As shown in the diagram on the right, the difference between the unlensed angular position and the observed position is this deflection angle, reduced by a ratio of distances, described as the lens equation
This Newtonian form of the lens equation can be derived by using a similarity between triangles P 1 P O1 F 1 and L 3 L 2 F 1 and another similarity between triangles L 1 L 2 F 2 and P 2 P 02 F 2 in the right figure. The similarities give the following equations and combining these results gives the Newtonian form of the lens equation.
Albert Einstein predicted in 1936 that rays of light from the same direction that skirt the edges of the Sun would converge to a focal point approximately 542 AU from the Sun. [37] Thus, a probe positioned at this distance (or greater) from the Sun could use the Sun as a gravitational lens for magnifying distant objects on the opposite side of ...
In pre-relativistic physics the ability should decrease at high velocities, because the time in which ionizing particles in motion can interact with the electrons of other atoms or molecules is diminished; however, in relativity, the higher-than-expected ionization ability can be explained by length contraction of the Coulomb field in frames in ...
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton's Principia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force.
The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics could encompass both.