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off the micrometer value and note down the re-
sult l
.
M
•
To be able to discern any errors in counting the
rings, steps 1-3 should be repeated at least 3 times.
5.1.3 Experiment evaluation
•
If, for example, during initial measurement m = 30
rings were counted and 20 mm – l
is the measured distance then, for gearing of
1:830, the path distance to the mirror is found to
be l
= 9761 nm and therefore the wavelength is:
S
2
l
λ =
s
=
651
nm
m
•
Assuming the experiments are performed with
care the results of all the measurements should
deviate from the mean value by no more than
2%. If greater deviations are discovered then the
eccentric may need cleaning (see Section 3, ec-
centric cleaning and maintenance).
•
The measurement result for the wavelength
should be accurate to at least ± 5%. It is also pos-
sible to perform a check using a laser with a known
wavelength (He-Ne Laser: λ = 632.8 nm).
5.2 Refractive index of glass
5.2.1 Experiment setup
•
The experiment setup initially corresponds to the
standard experiment setup (see Section 5.1.1).
Subsequently the glass plate with the revolving
holder is mounted in the portion of beam at the
front as shown in Fig. 3. The adjustable mirror is
then minimally readjusted until the interference
rings are positioned in the middle of the screen.
Fig. 3: Experiment setup for measuring the refractive index of glass
•
If the mirror is now rotated slightly back and forth
around the region of 0°, the transition between
when interference rings appear and disappear
should be precisely at 0°. If this is not the case,
then the beam splitter is not positioned precisely
at a 45° angle with respect to the finely adjust-
able mirror. However, since a completely precise
alignment of the beam splitter is practically im-
possible, note down the angle φ
sition between when interference rings appear
and disappear does take place. During the evalu-
ation this angle is subtracted from the measured
value φ
to obtain the actual rotation angle φ.
M
5.2.2 Measurement procedure
•
The glass plate is slowly rotated starting from the
angle φ
. In the course of this action the number
0
1) C. L. Andrews, Optics of the Electromagnetic Spectrum, Prentice-Hall, 1960
= 11.76 mm
M
at which the tran-
0
10
of rings is counted as they disappear. The larger
the angle rotated the smaller the change in angle
that causes a ring to disappear. Consequently you
need to have a very steady hand to count more
than approx. 20 rings.
5.2.3 Experiment evaluation
•
Taking the angle φ (e.g. 5.4°), the measured num-
ber of rings m (e.g. 20), the wavelength λ (in air)
of the laser being used (e.g. 633 nm) and the thick-
ness of the glass disk t (here 4 mm) we obtain from
Andrews' expression
1)
glass:
−
λ
) −
(
(
2
t m
1
=
n
G
−
(
2 1
t
•
When comparing your own results with those
found in the literature always bear in mind that
the refractive index is a function of the wavelength
and consequently only values for the same wave-
lengths are comparable.
5.3 Refractive index of air
5.3.1 Experiment setup
•
The experiment setup corresponds initially to the
standard experiment setup (see Section 5.1.1) with
the only change that here it is expedient to have
the partially reflecting surface of the beam split-
ter pointing to the right and rearwards. The
vacuum cell is now placed in the right-hand beam
as in Fig. 4 and the adjustable mirror is minimally
adjusted again to bring the interference rings into
the center of the screen.
Fig. 4: Experiment setup for measuring refractive index of air
5.3.2 Measurement procedure
•
Connect the vacuum pump to the vacuum cell and
note down the displayed pressure p. Then slowly
evacuate the cell and count the number of rings
m as they disappear. The number of rings that
have disappeared for a certain pressure is recorded
at regular pressure intervals. When the minimum
pressure has been reached (about 10 kPa for a
simple hand pump), the vacuum cell is filled with
air again. A set of measurements can now be made
for pressure over atmospheric (up to max. 200 kPa
corresponding to 1 bar over atmospheric).
the refractive index n
of
G
2 2
λ
m
φ
) +
cos
4
t
=
1 55
.
φ
) −
λ
cos
m
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