Chapter 9

Geometrical and waves optics

Twyman's interferometer

Take 20 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.

The device is a Michelson interferometer in which the mirror is a convex spherical mirror of large radius ; the mirror is plane and the beginning :

The source placed at object focus, is bit extended.

It is monochromatic wavelength of .

Twyman's interferometer

Question

What kind of fringes do we observe ?

Where are they located ?

What is the role of the lens ?

Hint

Solution

It uses the equivalent diagram of the Michelson (see figure). The spherical mirror is replaced by its symmetrical with respect to the splitter.

A ray arrives at normal incidence on the mirror and goes down ; a similar beam is reflected on the mirror according to the laws of reflection.

Interference is located on the mirrors.

The lens serves to form the image of the mirrors (and fringes) on a screen.

The path difference between the two rays arriving at is :

But by stigmatism :

So :

Yet :

Finally :

Twyman's interferometer

Question

Determine the radius of the bright fringe.

Hint

Solution

The bright fringes are rings (Newton's rings), whose radii are given by :

Is :

For the rays seen on the screen, we have to take into account the magnification due to the lens.

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