Snell’s laws

The physics of X-ray refraction are analogous to the well known refraction of light by optical lenses and prisms, governed by Snell s law. The special feature is the deflection at very small angles of few minutes of arc, as the refractive index of X-rays in matter is nearly one. Due to the density differences at inner surfaces most of the incident X-rays are deflected [1]. As the scattered intensity of refraction is proportional to the specific surface of a sample, a reference standard gives a quantitative measure for analytical determinations. 

The geometry of Fig. 10.3 leads to a result known as Snell s law, which relates the refractive index of the medium to the angles formed by two wave fronts with the interface. Defining 6q and 6, respectively, as the angles between the phase boundary and the wave front under vacuum and in the medium of refractive index n, show that Snell s law requires n = sin Oo/sind. 

Reflection and refraction of X-rays follow the laws of optics (Fig. 4.2) The glancing angles of incidence (i) and reflection ( ) are equal. The respective refraction angles follow Snell s law for different phase velocities v in mediums 1 and 2 ... 

From Snell s Law, sin(0j) m = sin(0j) nr. We have TIR when sin(Oj) > nr/rii, while we will have refraction and reflection when sin(0j) < nr/ni. In practical cases properties of light, such as phase, polarization and intensity, can be modulated inside the wave guide by a given measurand, which is interacting, for instance, with a CIM lying within the penetration depth for the evanescent field of the light localized near the external guide surface. 

The phenomenon of SPR is directly related to Snell s Law (see fig. 18). In fact when radiation passes to a medium with lower dielectric constant there is a critical angle beyond which the refracted beam cannot propagate in the other medium. 

At point A in Figure 2.2, a ray of white light enters the medium and its velocity diminishes, with the result that its path is bent towards the normal at this point. Snell s law of refraction states that the relation between the angles of incidence (i) and refraction (r) is given by Equation 2.1, where n is the ratio of refractive indices of the medium and air. 

Light is refracted, or bent, as it passes between media with different refractive indices. Snell s Law describes refraction mathematically as... 

Whenever a beam of light enters from a rarer (air) medium into a denser medium (glass or liquid) it bends towards the normal. Conversely, the beam of light is deflected away from the normal when it leaves a denser medium to enter a rarer medium (Fig. 1.8). According to Snell s Law... 

The maximum input acceptance angle for a fiber-optic cable is determined by the critical angle for total internal reflection, which is given by Snell s law ... 

The RI detector is a commonly used universal detector that measures a physical property of the bulk medium. RI is the physical parameter that characterizes the velocity of light in a medium and is nsed to describe the behavior of light as it passes between different materials. The deflection, or refraction, of light as it crosses the boundary between materials with different refractive indices is given by Snell s law ... 

We also have 0r = 0, from the law of specular reflection, and 0, is determined from the generalized Snell s law ... 

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