1) Destructive interference
The condition for constructive interference to occur is:
(1)
where
is the path difference, with
is the distance of the point from the first source
is the distance of the point from the second source
m is an integer number
is the wavelength
In this problem, we have
So let's use eq.(1) to see if the resulting m is an integer
It is not an integer so constructive interference does not occur.
Let's now analyze the condition for destructive interference:
(2)
If we apply the same procedure to eq.(2), we find
which is an integer: so, this point is a point of destructive interference.
2) Constructive interference
In this case we have
So the path difference is
Using the condition for constructive interference:
Which is an integer, so this is a point of constructive interference.
3) Destructive interference
In this case we have
So the path difference is
Using the condition for constructive interference:
This is not an integer, so this is not a point of constructive interference.
So let's use now the condition for destructive interference:
which is an integer: so, this point is a point of destructive interference.