scientific
Interferometer
012-02675B
10
Analyzing Your Data
As the laser beam passes back and forth between the beam-splitter and the fixed mirror, it
passes twice through the vacuum chamber. Outside the chamber the optical path-lengths of the
two interferometer beams do not change throughout the experiment. Inside the chamber,
however, the wavelength of the light gets longer as the pressure is reduced.
Suppose that originally the chamber length d was 10 wavelengths long (it is actually much
longer). As you slowly pump out the chamber, the wavelength increases until, at some point,
the chamber is only 9-1/2 wavelengths long. Since the laser beam passes twice through the
chamber, the light now goes through one less oscillation as it passes through the chamber.
This has the same effect on the interference pattern as when the movable mirror is moved
toward the beam-splitter by 1/2 wavelength. A single fringe will have passed by the reference
mark on the viewing screen.
Originally there are m
i
= 2 d/
λ
i
wavelengths of light within the chamber (counting both passes
of the laser beam). At the final pressure there are m
f
= 2 d/
λ
f
wavelengths within the chamber.
The difference between these values, m
i
= m
f
, is just
∆
m, the number of fringes you counted
as you evacuated the chamber. Therefore:
∆
m = 2 d/
λ
i
- 2d/
λ
f
However,
λ
i
=
λ
o
/n
i
and
λ
f
=
λ
o
/n
f
; where n
i
and n
f
are the initial and final values for the
refraction index of the air inside the chamber. Therefore
∆
m = 2 d (n
i
= n
f
) /
λ
o
, so that n
i
- n
f
=
∆
m
λ
o
/2d. The slope of the n vs pressure graph is therefore calculated as:
n
i
- n
f
∆
m
λ
o
/2d
––––––––––
=
––––––––––––
P
i
- P
f
P
i
- P
f
where P
i
= the initial air pressure
P
f
= the final air pressure
n
i
= the index of refraction of air at P
i
n
f
= the index of refraction of air at P
f
∆
m = the number of fringes that passed the reference point during evacuation
λ
o
= the wavelength of the laser light in vacuum (obtain this value from your teacher)
d = the length of the vacuum chamber (3.0 cm)
➇
Calculate the slope of the n vs pressure graph for air.
➈
On a separate piece of paper, draw the n vs pressure graph. From your graph, what is n
atm
, the
refraction index for air at a pressure of 1 atmosphere (76 cm Hg).
n
atm
= ______________
➦
NOTE: Remember that at zero pressure, n = 1 exactly. Using this as a fixed data point, use
your calculated slope to construct the graph. The slope will be very slight, since large
pressure changes result in very small changes in n. Adjust the scale of your graph as needed
so that you can accurately determine the small shift in n that occurs between zero pressure
and atmospheric pressure.
