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Partial transmission and reflection of a wave.
Partial transmission and reflection of a wave.

The Fresnel equations, deduced by Augustin-Jean Fresnel (pronounced /freɪˈnɛl/), describe the behaviour of light when moving between media of differing refractive indices. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 An optical medium is material through which Electromagnetic waves propagate The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium The reflection of light that the equations predict is known as Fresnel reflection. Reflection is the change in direction of a Wave front at an interface between two different media so that the wave front returns into the medium from which

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Explanation

When light moves from a medium of a given refractive index n1 into a second medium with refractive index n2, both reflection and refraction of the light may occur. The refractive index (or index of Refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves is reduced inside the medium Refraction is the change in direction of a Wave due to a change in its Speed.

Variables used in the Fresnel equations.
Variables used in the Fresnel equations.

In the diagram on the right, an incident light ray PO strikes at point O the interface between two media of refractive indexes n1 and n2. In Optics, a ray is an idealized narrow Beam of light. Rays are used to model the propagation of Light through an optical system by dividing the real light Part of the ray is reflected as ray OQ and part refracted as ray OS. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θi, θr and θt, respectively. The relationship between these angles is given by the law of reflection and Snell's law. Specular reflection is the perfect Mirror -like reflection of light (or sometimes other kinds of Wave) from a surface in which light from a single incoming In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship

The fraction of the intensity of incident light that is reflected from the interface is given by the reflection coefficient R, and the fraction refracted by the transmission coefficient T. In Physics, intensity is a measure of the time-averaged Energy Flux. The reflection coefficient is used in Physics and Electrical engineering when Wave propagation in a medium containing discontinuities is considered See also Reflection coefficient The transmission coefficient is used in physics and electrical engineering when Wave propagation in a medium containing The Fresnel equations, which are based on the assumption that the two materials are both non-magnetic, may be used to calculate R and T in a given situation. The following fields are continuous: tangential E and H, normal B and D.

The calculations of R and T depend on polarisation of the incident ray. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations If the light is polarised with the electric field of the light perpendicular to the plane of the diagram above (s-polarised), the reflection coefficient is given by:

R_s = \left[ \frac{\sin (\theta_t - \theta_i)}{\sin (\theta_t + \theta_i)} \right]^2=\left[\frac{n_1\cos(\theta_i)-n_2\cos(\theta_t)}{n_1\cos(\theta_i)+n_2\cos(\theta_t)}\right]^2

where θt can be derived from θi by Snell's law. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can

If the incident light is polarised in the plane of the diagram (p-polarised), the R is given by:

R_p = \left[ \frac{\tan (\theta_t - \theta_i)}{\tan (\theta_t + \theta_i)} \right]^2=\left[\frac{n_1\cos(\theta_t)-n_2\cos(\theta_i)}{n_1\cos(\theta_t)+n_2\cos(\theta_i)}\right]^2

The transmission coefficient in each case is given by Ts = 1 − Rs and Tp = 1 − Rp.

If the incident light is unpolarised (containing an equal mix of s- and p-polarisations), the reflection coefficient is R =  (Rs + Rp)/2.

The reflection and transmission coefficients correspond to the ratio of the intensity of the incident ray to that of the reflected and transmitted rays. In Physics, intensity is a measure of the time-averaged Energy Flux. Equations for coefficients corresponding to ratios of the electric field amplitudes of the waves can also be derived, and these are also called "Fresnel equations". In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system

At one particular angle for a given n1 and n2, the value of Rp goes to zero and a p-polarised incident ray is purely refracted. This angle is known as Brewster's angle, and is around 56° for a glass medium in air or vacuum. Brewster's angle (also known as the polarization angle) is an Angle of incidence at which light with a particular Polarization is perfectly transmitted Note that this statement is only true when the refractive indexes of both materials are real numbers, as is the case for materials like air and glass. In Mathematics, the real numbers may be described informally in several different ways For materials that absorb light, like metals and semiconductors, n is complex, and Rp does not generally go to zero. The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted

When moving from a more dense medium into a less dense one (i. e. , n1 > n2), above an incidence angle known as the critical angle, all light is reflected and Rs = Rp = 1. This phenomenon is known as total internal reflection. The critical angle is approximately 41° for glass in air.

Image:fresnel2.png

When the light is at near-normal incidence to the interface (θi ≈ θt ≈ 0), the reflection and transmission coefficient are given by:

R = R_s = R_p = \left( \frac{n_1 - n_2}{n_1 + n_2} \right)^2
T = T_s = T_p = 1-R = \frac{4 n_1 n_2}{\left(n_1 + n_2 \right)^2}

For common glass, the reflection coefficient is about 4%. Note that reflection by a window is from the front side as well as the back side, and that some of the light bounces back and forth a number of times between the two sides. The combined reflection coefficient for this case is 2R/(1 + R), when interference can be neglected. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern

In reality, when light makes multiple reflections between two parallel surfaces, the multiple beams of light generally interfere with one another, and the surfaces act as a Fabry-Perot interferometer. This effect is responsible for the colours seen in oil films on water, and it is used in optics to make optical coatings that can greatly lower the reflectivity or can be used as an optical filter. An optical coating is a thin layer of material deposited on an optical component such as a lens or Mirror, which alters the way in which the optic Anti-reflective or antireflection (AR coatings are a type of Optical coating applied to the surface of lenses and other optical devices to reduce An optical filter is a device which selectively transmits light having certain properties (often a particular range of Wavelengths that is range of Colours

It should be noted that the discussion given here assumes that the permeability μ is equal to the vacuum permeability μ0 in both media. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. This is approximately true for most dielectric materials, but not for some other types of material. A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. The completely general Fresnel equations are more complicated.

See also

References

External links

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