For the central bright fringe, the path difference is 0.
S_{2}O
- S_{1}O = 0.
For the first bright fringe
S_{2}Q
- S_{1}Q =
l
Notice that in the triangle S_{1}S_{2}Z, S_{2}Z is l.
We know that S_{1}S_{2} is s.
Therefore:
sin
q
=
l/s.
For the triangle OPQ,
tan
f
= w/D.
Although in this diagram, it is clear that
q
¹
f, in the real thing, we can assume that
q =
f,
as the real set up is very much longer.
We know that for small angles
sin
q = tan
q.
Therefore:
To produce easily measurable
fringes, D must be large i.e. in
metres while s is small (<1 mm).
The larger D is the less bright the
fringes. We can increase the width
of the fringes by increasing the wavelength, or by decreasing the slit width.
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