Question

Consider red light with a wavelength of 692 nm in air that is incident onto two slits such that it gives diffraction fringes that are 1.00 mm apart on a screen at a distance L from the slits. If the screen is moved back by an additional 4.00 cm, the fringes become 1.20 mm apart. What is the separation between the slits?

Answer 1

The separation between slits is:

`d=0.1384 \, mm`

Step-by-step explanation:

The distance between adjacent maxima is given by the following expression:

`\Delta y=(\lambda L)/(d)`

For the distance between maxima being 1mm (let's solve all this problem using milimeters) we have the following:

`1=(L\lambda)/(d)` (1)

For the second condition in which the screen is moved 40 mm away we have the following:

`1.20=((L+40)\lambda)/(d)` (2)

Using equation 1 we can write:

`L=(L)/(d)`

Plugging the value of L in equation 2 brings us to

`1.20=(\lambda\left((d)/(\lamda)+40\right))/(d)`

`\implies 1.20=(d+40\lambda)/(d)`

`\implies 1.20d=d+40\lambda`

`\implies d=(40\lambda)/(0.20)=0.1384\, mm`

We could also as a bonus find L which is just

`L=(d)/(\lambda)`

I'll leave that up to you! Good luck!