Chapter 9

Geometrical and waves optics

Temporal coherence and Young slits ; displacement and interference fringes 

Take 15 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

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Consider the interference device of Young slits, with observation in the focal plane of a convergent thin lens .

We give :

Young slits


Describing the figure of interference observed and the intensity distribution .



The result is classical (see the review of the lecture). The particular interfringe is :

The intensity is given by the Fresnel's formula :


We interpose in the path of one of the beams the blade of parallel faces of thickness of and of index .

The faces are perpendicular to the axis of symmetry.

Determine the number fringes which defiled in .

We take :



The new path difference is :

The position of the central fringe becomes (it is obtained for a path difference of zero) :

The fringe has not changed and the number of fringes that defiled :


The blade is removed with parallel faces.

The slots are now illuminated by the yellow doublet of sodium formed by two radiation assumed monochromatic and same intensity, wavelength :


How far from the central fringe do the fringes disappear for the time ?



Qualitatively, the first interference appears when a dark fringe corresponding to is superimposed on a bright fringe associated with or for a verified interference of order :

Or :


We can deduce :

Then the value of the abscissa where the interference occurs :

Where were asked :

The average value of the two wavelengths.

Observation of double stars
The Michelson configuration "air blade" ("lame d'air", in french)