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The Goos–Hänchen effect (named after Hermann Fritz Gustav Goos (1883–1968) and Hilda Hänchen (1919–2013) is an optical phenomenon in which linearly polarized light undergoes a small lateral shift when totally internally reflected. The shift is perpendicular to the direction of propagation in the plane containing the incident and ...
The phase shift of the reflected wave on total internal reflection can similarly be obtained from the phase angles of r p and r s (whose magnitudes are unity in this case). These phase shifts are different for s and p waves, which is the well-known principle by which total internal reflection is used to effect polarization transformations .
The calculation of the phase shift was also a landmark in the application of complex numbers. Leonhard Euler had pioneered the use of complex exponents in solutions of ordinary differential equations , on the understanding that the real part of the solution was the relevant part. [ 33 ]
A ray of light being refracted through a glass slab Refraction of a light ray. In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refracted, when entering a ...
The calculation of glass properties allows "fine-tuning" of desired material characteristics, e.g., the refractive index. [1]The calculation of glass properties (glass modeling) is used to predict glass properties of interest or glass behavior under certain conditions (e.g., during production) without experimental investigation, based on past data and experience, with the intention to save ...
Soda–lime glass (for containers) [2] Borosilicate (low expansion, similar to Pyrex, Duran) Glass wool (for thermal insulation) Special optical glass (similar to Lead crystal) Fused silica Germania glass Germanium selenide glass Chemical composition, wt% 74 SiO 2, 13 Na 2 O, 10.5 CaO, 1.3 Al 2 O 3, 0.3 K 2 O, 0.2 SO 3, 0.2 MgO, 0.01 TiO 2, 0. ...
Each optical element (surface, interface, mirror, or beam travel) is described by a 2 × 2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system.
The phase shift is =, which causes fringes to shift in proportion to and . At non-relativistic speeds, the Sagnac effect is a simple consequence of the source independence of the speed of light. In other words, the Sagnac experiment does not distinguish between pre-relativistic physics and relativistic physics.