Question

In a two-slit experiment, a third-order bright fringe is observed at an angle of 7.10° away from the centerline. if the wavelength of light is 595 nm, how far apart are the two slits?

Answer 1

The condition for constructive interference is in a double slit experiment is:

`dsin(\theta)=m\lambda`
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:

`r_2-r_1 = dsin(\theta)`
For constructive interference to happen this difference must be equal to multiple of the wavelength.

`dsin(\theta)=m\lambda`
Now, let's calculate the answer:

`d=(m\lambda)/(sin\theta)`
When we plug in the number we get:

`d=0.014 $mm`