SE-9654
Zeeman Effect Experiment
8
012-14266B
where only two terms in the Taylor series expansion (cos
= 1 -
2
/2! +...) are kept because
is very small. The two rays will
be in phase and produce an interference maximum if and only if the following:
l = (n ± k)
, where k = 0, 1, 2, 3...
and n is a large integer approximately equal to 2d/
. Equation 8 then yields:
where
k
is the angle to the kth ring in the interference pattern (see
Figure 3 where k = 0 for the innermost ring). Here the negative
sign must be chosen for the (n - k) term since as
increases, the
left of Equation 9 decreases. Thus, the right hand side must
decrease as k increases.Note that the Fabry-Perot interferometer
can measure much smaller changes in
because
is multiplied by
a large n resulting in a much larger change in
. This increases its
resolution by roughly 2d/
~ 10
4
.
Final Theory
The camera has a focal length, f. Since the angle is small,
k
= R
k
/f to a very
good approximation and Equation 9 becomes:
We do not know the effective focal length, f, but we can use the B = 0 pattern
shown in Figure 3 to evaluate it. For the k = 0 ring, Equation 10 becomes:
Subtracting Equation 10 from Equation 11 gives:
l
DA AB CB
–
+
d
cos
------------
d
cos
------------
2d
sin
tan
–
+
2d
cos
------------
2d
2
sin
cos
--------------------
–
=
=
=
l
2d 1
2
sin
–
cos
----------------------------------
2d
cos
2d 1
2
2
-----
–
Eqn. 8
=
=
=
2
2 1
where k = 0, 1, 2, 3... Eqn. 9
2
k
d
n k
Figure 3: B = 0 Pattern
k = 0
k = 1
k = 2
k = 3
k = 4
Figure 4: Camera Geometry
where k = 1, 2, 3 ... Eqn. 10
2
k
2
R
2d 1
n k
2f
2
0
2
2
1
Eqn. 11
2
R
d
n
f