# The refractive index

### Refractive index microscope

Snell's law was originally defined by the relationship between the incident angles and the ratio of the velocities of light in the two media. There are several important points that can be drawn from this equation. This effect is termed dispersion and is responsible for chromatic aberration in microscope objectives. We should not be surprised at this, because the damping we put in for the oscillators is indeed a friction force and must be expected to cause a loss of energy. The variation of refractive index with wavelength for various glasses. The same kind of observations tell us about the materials in the stars. Why is there no field there? It certainly does not start off in the opposite direction when the field is first turned on. As the wave goes through the material, it is weakened. In other words, the diffracted wave is the same as though the hole were a new source.

A consequence of this phenomenon is that each wavelength experiences a slightly different degree of refraction when a heterogeneous light beam containing more than one frequency enters or leaves the medium.

Our dispersion equation suggests other interesting effects.

## Refractive index of glass prism

When n 1 is greater than n 2 , the angle of refraction is always larger than the angle of incidence. Also, the exponent is negative, so the factor is a real number less than one. See also Radio Propagation and Skywave. Main article: Dispersion optics The refractive index of materials varies with the wavelength and frequency of light. We imagine that the plugs are of exactly the same material as the wall. You know, of course, that a thin enough sheet of the most opaque material, even gold, is transparent. Dispersion also causes the focal length of lenses to be wavelength dependent. How does the charge happen to be going in the opposite direction? From such measurements we know that the chemical elements in the sun and in the stars are the same as those we find on the earth. The node of a wave is not a signal by itself.

It seems like an amazing backwards-forwards argument. These excellent properties make them a type of significant materials for infrared optics. In a perfect wave, which has no modulations of any kind, i. We should remark that our analysis of the refractive index gives a result that is somewhat simpler than you would actually find in nature.

In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.

We can see what such a complex index means when there is only one resonant frequency by going back to Eq. The index of refraction as a function of frequency.

Also, the exponent is negative, so the factor is a real number less than one. We shall now use this knowledge to find out how much energy is carried by a light wave.

## Refractive index of prism

However, some net energy will be radiated in other directions or even at other frequencies see scattering. It can be shown, however, that the speed at which you can send a signal is not determined by the index at one frequency, but depends on what the index is at many frequencies. To find what motion we expect for the electrons, we will assume that the atoms are little oscillators, that is, that the electrons are fastened elastically to the atoms, which means that if a force is applied to an electron its displacement from its normal position will be proportional to the force. There are several important points that can be drawn from this equation. In quantum mechanics even an atom with one electron, like hydrogen, has several resonant frequencies. The sign is not too interesting, since we are usually interested in intensity which is proportional to the square of the field. So for a gas, the index is nearly constant.

We should not be surprised at this, because the damping we put in for the oscillators is indeed a friction force and must be expected to cause a loss of energy. We have to explain the reason for that, because the hole is, of course, just where there are no sources, where there are no accelerating charges.

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