Temporal coherence and Young slits ; displacement and interference fringes
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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 :
Question
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 :
Question
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 :
Question
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 :
and
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 :
and
We can deduce :
Then the value of the abscissa where the interference occurs :
Where were asked :
The average value of the two wavelengths.
