# Refractive index and critical angle relationship theorems

### BBC Bitesize - Higher Physics - Refraction of light - Revision 3

In optics, the refractive index or index of refraction of a material is a dimensionless number that . Main article: Ewald–Oseen extinction theorem As the refractive index varies with wavelength, so will the refraction angle as light of the wavelength dependence of the refractive index, the Sellmeier equation can be used. reflectance near the critical angle in a prism–colloid interface does not have a sharp . questioned above the use of an effective refractive index in Fresnel's relations for the reflection theorem, it is not difficult to show that. Snell's law states the relationship between angles and indices of refraction. Total internal reflection occurs for any incident angle greater than the critical angle.

A few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodiumwith a wavelength of nanometersas is conventionally done.

## Snell's law

Almost all solids and liquids have refractive indices above 1. Aerogel is a very low density solid that can be produced with refractive index in the range from 1.

Most plastics have refractive indices in the range from 1. Moreover, topological insulator material are transparent when they have nanoscale thickness. 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. If at any time the values for the numerator and denominator become accidentally switched, the critical angle value cannot be calculated. Mathematically, this would involve finding the inverse-sine of a number greater than 1. Physically, this would involve finding the critical angle for a situation in which the light is traveling from the less dense medium into the more dense medium - which again, is not possible.

This equation for the critical angle can be used to predict the critical angle for any boundary, provided that the indices of refraction of the two materials on each side of the boundary are known. Examples of its use are shown below: Example A Calculate the critical angle for the crown glass-air boundary.

### Snell's Law .docx | Youssef Abdouni - bestwebdirectory.info

Refer to the table of indices of refraction if necessary. The solution to the problem involves the use of the above equation for the critical angle. Of all the possible combinations of materials that could interface to form a boundary, the combination of diamond and air provides one of the largest differences in the index of refraction values. This peculiarity about the diamond-air boundary plays an important role in the brilliance of a diamond gemstone. Having a small critical angle, light has the tendency to become "trapped" inside of a diamond once it enters.

A light ray will typically undergo TIR several times before finally refracting out of the diamond. Because the diamond-air boundary has such a small critical angle due to diamond's large index of refractionmost rays approach the diamond at angles of incidence greater than the critical angle.

This gives diamond a tendency to sparkle. The effect can be enhanced by the cutting of a diamond gemstone with a strategically planned shape.

## Refractive index

The diagram below depicts the total internal reflection within a diamond gemstone with a strategic and a non-strategic cut. Use the Find the Critical Angle widget below to investigate the effect of the indices of refraction upon the critical angle. Simply enter the index of refraction values; then click the Calculate button to view the result.

Use the widget as a practice tool. Check Your Understanding 1. Suppose that the angle of incidence of a laser beam in water and heading towards air is adjusted to degrees. Use Snell's law to calculate the angle of refraction? Explain your result or lack of result. See Answer Good luck! This problem has no solution.

**Refraction (4 of 5) Calculating the Critical Angle**

The angle of incidence is greater than the critical angle, so TIR occurs.