optics - Relation between intensity of light and refractive index - Physics Stack Exchange
Refractive index is calculated and their variations with wavelength and . photon energy is low, the relation between the absorption coefficient. In optics, the refractive index or index of refraction of a material is a dimensionless number that As a result, the energy (E = h f) of the photon, and therefore the perceived While the refractive index affects wavelength, it depends on photon .. the complex refractive index are related through the Kramers–Kronig relations. The energy of light is related to its frequency and velocity as follows: Note that from the equation given above- The refractive index of any material depends on the wavelength of light because different wavelengths are.
Most plastics have refractive indices in the range from 1. Moreover, topological insulator material are transparent when they have nanoscale thickness.
Refractive index - Wikipedia
These excellent properties make them a type of significant materials for infrared optics. The refractive index measures the phase velocity of light, which does not carry information.
This can occur close to resonance frequenciesfor absorbing media, in plasmasand for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies. Since the refractive index of the ionosphere a plasmais less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.
See also Radio Propagation and Skywave. Negative index metamaterials A split-ring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values.
The resulting negative refraction i. Ewald—Oseen extinction theorem At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.
Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility. As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency. The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity.
Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies see scattering. Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities: This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.
This is called "anomalous refraction", and is observed close to absorption lines typically in infrared spectrawith X-rays in ordinary materials, and with radio waves in Earth's ionosphere. An unpolarized beam of light, vibrating in all directions perpendicular to its path strikes such a surface and is reflected. The reflected beam will be polarized with vibration directions parallel to the reflecting surface perpendicular to the page as indicated by the open circles on the ray path.
If some of this light also enters the material and is refracted at an angle 90o to the path of the reflected ray, it too will become partially polarized, with vibration directions again perpendicular to the path of the refracted ray, but in the plane perpendicular to the direction of vibration in the reflected ray the plane of the paper, as shown in the drawing.
Polarization can also be achieved by passing the light through a substance that absorbs light vibrating in all directions except one. Anisotropic crystals have this property in certain directions, called privileged directions, and we will discuss these properties when we discuss uniaxial and biaxial crystals. Crystals were used to produce polarized light in microscopes built before about The device used to make polarized light in modern microscopes is a Polaroid, a trade name for a plastic film made by the Polaroid Corporation.
A Polaroid consists of long-chain organic molecules that are aligned in one direction an placed in a plastic sheet. They are placed close enough to form a closely spaced linear grid, that allows the passage of light vibrating only in the same direction as the grid.
Light vibrating in all other directions is absorbed.
Such a device is also called a polarizer. If a beam on non-polarized light encounters a polarizer, only light vibrating parallel to the polarizing direction of the polarizer will be allowed to pass. The light coming out on the other side will then be plane polarized, and will be vibrating parallel to the polarizing direction of the polarizer.
If another polarizer with its polarization direction oriented perpendicular to the first polarizer is placed in front of the beam of now polarized light, then no light will penetrate the second polarizer. In this case we say that the light has been extinguished. Polaroid sunglasses use these same principles.
For example, incoming solar radiation is reflected off of the surface of the ocean or the painted hood of your car. Reflected light coming off of either of these surfaces will be polarized such that the vibration directions are parallel to the reflected surface, or approximately horizontal as in the first method of polarization discussed above. Polaroid sunglasses contain polarizers with the polarization direction oriented vertically. Wearing such glasses will cut out all of the horizontally polarized light reflecting off the water surface or hood of your car.
The Polarizing Microscope In optical mineralogy we use a microscope called a polarizing microscope. Such a microscope is equipped with two polarizers that are normally oriented so that their polarization directions are perpendicular to one another. Light from a light source located below the tube and stage of the microscope is initially unpolarized. This light first passes through the lower polarizer usually just called the polarizerwhere it becomes polarized such that the light is vibrating from the users right to left.
These directions are referred to as East right and West left. The light then passes through a hole in the rotatable stage of the microscope and enters the lower lens, called the objective lens. Mounted within the microscope tube is a second polarizer, called the analyzer, that can be rotated or pushed so that in can be in the light path inserted position or not in the light path analyzer out position.Wavelength, Frequency, Energy, Speed, Amplitude, Period Equations & Formulas - Chemistry & Physics
The analyzer has a polarization direction exactly perpendicular to that of the lower polarizer These directions are usually referred to as North - South. If the analyzer is in, then the plane polarized light coming from the lower polarizer will be blocked, and no light will be transmitted though the ocular lens above. If the analyzer is out, so that it is not in the light path, then the polarized light will be transmitted through the ocular lens.
Next time we will see how this microscope is used to examine isotropic substances and determine their refractive indices.
Isotropic Substances As discussed above, isotropic substance are those wherein the velocity of light or the refractive index does not vary with direction in the substance. Substances such as gases, liquids, glasses, and minerals that crystallize in the isometric crystal system are isotropic.
We here introduce the concept of the optical indicatrix then look at what we see when we look at isotropic substances through the polarizing microscope. We then see how to determine the refractive index of isotropic substances as a means to identify them, and then take a first look at uniaxial materials.
The Isotropic Indicatrix The concept of the optical indicatrix is important as a visual means of looking at the way refractive index varies with direction in a substance. For isotropic minerals and substances the indicatrix is pretty trivial, since the refractive index does not vary with direction. The optical indicatrix is simply a three dimensional object constructed by drawing vectors of length proportional to the refractive index for light vibrating parallel to the vector direction from a central point.
The ends of all of the vectors are then connected to form the indicatrix. For isotropic minerals the indicatrix is a sphere as can be seen here. The indicatrix can be placed anywhere within or on a crystal so long as the crystallographic directions in the indicatrix are moved parallel to themselves. Again, for the isotropic indicatrix, this is fairly trivial since the refractive indices do not correspond to crystallographic directions and the refractive indices are the same in all directions, but the usefulness of the indicatrix concept will become much more clear when we look at anisotropic substances.
Isotropic Substances and Polarized Light As discussed last time, the polarizing microscope has two polarizers. The lower polarizer often just called the polarizer is above the light source, and thus creates polarized light that vibrates in the East West direction. The upper polarizer, called the analyzer, is polarized to create polarized light vibrating at 90o to that produced by the lower polarizer. Thus, if there is only air, an isotropic substance, between the two polarizers, the E-W vibrating light is completely eliminated at the analyzer, and no light passes through the ocular lens.
So, if we place a mineral grain on a glass slide glass is also isotropicand view the grain through the ocular lens with the analyzer not inserted in the light path, we will be able to clearly see the grain.
Relationship between wavelength and refraction
If the grain selectively absorbs light of certain wavelengths, then the grain will show its absorption color. If we now insert the analyzer in the light path, the light coming out of the grain will still be polarized in an E-W direction, since isotropic substances do not change the polarization direction, and the analyzer will cut out all of this light. Thus, no light coming out of the mineral grain will pass through the analyzer.
The mineral is thus said to be extinct in this position. Similarly, if we rotate the stage of the microscope, and thus rotate the grain, it will remain extinct for all rotation positions. This is the primary means to determine whether or not a substance is isotropic. That is, rotate the grain on the microscope stage with the analyzer inserted.
If the grain remains extinct throughout a o rotation of the stage, then the mineral or substance on the microscope stage is probably isotropic.
Refraction of light
Determination of Refractive Index for Isotropic Solids: The Immersion Method In isotropic substances, there are only two optical properties that can be determined. One of these is the absorption color, as discussed above. The other is the refractive index.
Tables of refractive indices for isotropic minerals, list only the refractive index for one wavelength of light. The wavelength chosen is nm, which corresponds to a yellow color. Such a wavelength would be given off of a sodium vapor lamp. Since these are expensive and generate much heat, sodium vapor lamps are not generally used in optical mineralogy.
Instead we use white light. Still, as we shall see later, we can determine the refractive index for nm. The comparison materials used are called refractive index oils.
These are smelly organic oils that are calibrated over a range of refractive indices from 1. As you will see in lab, grains of the unknown substance are placed on a glass slide, a cover glass is placed over the grains, and a refractive index oil is introduced to completely surround the grains.
This is called the immersion method. The grains are then observed with the analyzer not inserted. If the grain has a refractive index that is very much different from the refractive index of the oil, then the grain boundaries will stand out strongly next to the surrounding oil. The grain will then be said to show high relief relative to the oil.
High relief indicates that the refractive index of the grain is very much different from the refractive index of the oil.