Chapter 9

# Michelson's rays

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.

A Michelson interferometer adjusted in blade air (thickness ) is illuminated by a point source of wavelength .

The output is placed a convergent lens of focal length and a screen in its image focal plane.

We reference on the screen bright rings whose radii are counted from the center :

 Bright ring 1 2 3 4 5 5,02 7,11 8,7 10 12

## Question

What is the path difference between two beams interfere in a point on the screen of a distance from the optical axis ?

Express as a function of , and .

### Solution

The path difference is : (see the lesson about the Michelson interferometer)

## Question

Deduce data the thickness of the air blade.

### Solution

As , we deduce that :

and fringes can be exploited : given that the order of interference decreases as further away from the center :

We deduce as :

## Question

What is the order of interference at the center ?

### Solution

is order at the center. It was "almost" a bright fringe at the center.

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The Michelson configuration "air blade" ("lame d'air", in french)
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Diffraction gratings