The condition for constructive interference is in a double slit experiment is:
[tex]dsin(\theta)=m\lambda[/tex]
Where d is the distance between two slits, m is a number of the fringe.
We know that difference in path length traveled by the two rays is approximately:
[tex]r_2-r_1 = dsin(\theta)[/tex]
For constructive interference to happen this difference must be equal to multiple of the wavelength.
[tex]dsin(\theta)=m\lambda[/tex]
Now, let's calculate the answer:
[tex]d=\frac{m\lambda}{sin\theta}[/tex]
When we plug in the number we get:
[tex]d=0.014 $mm[/tex]
