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
.
Question
What kind of fringes do we observe ?
Where are they located ?
What is the role of the lens
?
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 :
Question
Determine the radius
of the
bright fringe.
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.
