Q1, These 2 formulas are from Nelson's textbook, there are just a few things I am unsure of. The diagram is attached
1st formula:
[taking the central bright band as n = 0]
In a 2 slit Young's experiment:
is the angle that the nodal line makes with the centre line.
The formula has
in front of
which implies P must be a dark band.
What I'm wondering is, is this formula is a general formula for all dark bands for a 2 slit experiment? Ie, if I wanted to find the angle the 3rd nodal line makes with the centre line then
would become
.
But then, what if I wanted to find the angle an ANTI-nodal line makes with the centre line, would I change the formula to
? [Since the path difference for bright bands has co-efficient of "n" in front of
.] Ie, If I wanted to find the angle the 2nd antinodal makes with the centre line then it would be
(Since the centre bright band is n = 0). Or does the formula only work for nodal lines and hence dark bands?
Now, would this formula also work for single slit experiment? So instead of
and
being 2 separate slits, they are just the "corners" of a single slit. If it does work for a single slit, then would "
" just be the width of the single slit? Would it also work for finding out the angle an antinodal line makes with the centre line or does it have to be nodal lines?
2nd formula:
: distance of nodal point from centre line
: distance between the 2 slits.
: distance of nodal point to the centre of the 2 slits.
In a 2 slit experiment: Again, does this formula only work for nodal lines (hence dark bands)? Because the formula contains
which implies the band must be a dark band and as a result L is the length of the nodal line. So could you also use it to find out the distance of a bright band to the centre line. For example,
would just be "
" and
would just be the distance of the bright band to the centre of the 2 slits. Or is that totally wrong?
In a single slit experiment: Could this formula work for a single slit experiment? So instead of
and
being 2 separate slits, they are just the "corners" of a single slit. If it does work then is "
" the width of the single slit? And could you use it to find the distance of a bright band to the centre line? If so, "
" would be the length of the antinodal line right? Or does it only work for dark bands?