Undulatory optics

The undulatory optical is the discipline which studies the Lumière by regarding it as being a electromagnetic Onde . Undulatory optics sticks more particularly to the phenomena affecting the waves, like the Interférence S and the Diffraction.

Principle

The light to go from a point to another is propagated with a given speed. The light in a given point will be the coherent or incoherent addition electromagnetic Champ in this point at the moment T. This field is undulatory; that means that the light is a Onde being propagated with a certain speed. That has many effects different from the geometrical Optique. For example, one attends phenomena of Interférence and Diffraction. They occur when the sources are coherent between them: the way simplest to do it is to use only one source, to separate it in two beams, and to bring back them to the same place.

Example

Let us consider a Onde planes Monochromatique arriving on NR parallel slits. If the phenomena of diffraction are neglected, the total Amplitude is given by the relation:

\ frac {has \ cdot \ sin (NR \ cdot \ phi)}{\ sin (\ phi)}

The intensity is equal to the square of the amplitude:

\ left (\ frac {has \ cdot \ sin (NR \ cdot \ phi)}{\ sin (\ phi)}\ right) ^2

There is, for 7 slits, the curve: Thus the superposition of waves gives dark fringes (where the interference is destructive) and of the fringes more intense than the simple amount of the NR sources (where the interference is constructive). ; Demonstration :

the formula of the sum of a geometrical Suite

\ textstyle \ sum_ {k=0} ^ {n-1} r^k= \ frac {r^n-1} {r-1}

enables us to make the sum of the coherent signals resulting from the NR slits having all has like amplitude and out of phase chacuns compared to the following of

e^ {J \ cdot \ phi}

\ sum_ {k=0} ^ {N-1} has \ cdot e^ {J \ cdot K \ cdot \ phi} =A \ frac {e^ {J \ cdot NR \ cdot \ phi} - 1} {e^ {J \ cdot \ phi} - 1}

By using the relation of Bragg to express dephasing in the direction θ:

\ phi= \ frac {\ pi D} {\ lambda} \ sin \ theta

, one obtains:

I (\ theta) = I_0 \ left (\ frac {\ sin \ left (\ frac {NR \ pi D} {\ lambda} \ sin \ theta \ right)}{\ sin \ left (\ frac {\ pi D} {\ lambda} \ sin \ theta \ right)}\ right) ^2

where NR is the number of slits, D is the width of the slits, λ is the wavelength of the wave, and θ is the direction of the light after passage in the slits.

A case particuler: slits of Young

The case N=2 corresponds to two parallel slits. There is then the following curve: It is in fact a Sinusoïde. If one did not regard the light as undulatory, one would obtain only widened slits.

See too

Optical
geometrical Quantum optic
Optical
electromagnetism
Wave and Wavelength
Interference S
Diffraction and Theory of optical diffraction
Network
Diffraction pattern
Slits of Young

External bonds

'' undulatory Optique '' on the site of the university of Maine
Illustration showing that the electrons behave like the photons at the time of the interference of two sources
Site of the institute of optics