A Michelson interferometer consists of a 50/50 beam splitter (half of the light

Question

A Michelson interferometer consists of a 50/50 beam splitter (half of the light is transmitted, half is reflected) and two mirrors, as shown in the figure. By varying the relative path lengths, one can change the amount of light that leaves via the bottom exit 'port' of the interferometer. This enables one, e.g., to measure distances very accurately.

A 1-mW laser of wavelength ? = 350 nm, is directed into the interferometer. Initially the path lengths of the two arms are identical, so that all the light goes to the detector at the bottom (i.e., there's complete constructive interference of the waves from the two paths).

1)

How much does mirror M1 need to be moved (the minimum distance) so that no light will be detected at D1?

?x =

microns

2)

Now instead a 2-mW laser of wavelength ? = 700 nm is directed into the interferometer (with the mirror M1 at the displacement calculated in part a). How much power is detected at D1?

nW

3)

What is the minimum mirror displacement (not counting ?x = 0) such that the full power of both lasers would appear at the detector? (You don't need to worry about interference between the lasers, since they have such different colors.);

microns

4)

Assume that we now place a small cell of length 8 cm in one of the interferometer arms, as shown:

The cell, which has transparent glass windows, is initially filled with air (which at standard temperature and pressure has index of refraction nair = 1.0029). Now we use a vacuum pump to remove the air in the cell (so that n = 1 exactly). Approximately how many 'fringes' of the 350-nm laser are detected at D1 as the cell is being evacuated (i.e., how many times does the power at the detector reach a maximum)?

Explanation / Answer

art a you got, for part

b) you just divide the current intensity by two. The cos will work out to .5

c) The maximum intensity will occur again when the cos is at a max which is at 2 pi. We also know:

Phase/2 = (2 pi) * (dx) / wavelength
where we know phase = 2 pi

if we rearrange.....

dx = wavelength / 2

so plug in your wavelength and make sure to report your answer in microns

d) This is a nasty one and took a while.

you have the two different n's. and you know the length L.

Let:
Na = N of air
Nv = N of vacuum

(L * Na - L * Nv) * 2 / wavelength in vacuum

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