# 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.

If you have more questions, feel free to ask them on the forum.

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 .

### Hint

### Solution

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 :

### Hint

### Solution

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 ?

### Hint

### Solution

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.