Vertical double slit experiment separation of bright spots in air and water

[SilentBlade91]

Homework Statement

A scientist decides to do the double-slit experiment in a ver-
tical tube, with the slits at the top and a viewing screen at the
bottom as shown. With red light from a HeNe laser (632 nm) a
nice pattern forms on the viewing screen, with the bright spots
1.50 cm apart.

Now the scientist fills the tube up with water. What
is the separation of the bright spots now?

Homework Equations

(nw)/d=x/L
I think

The Attempt at a Solution

So we know n1 (air) is 1, and n2 (water) is 1.33. I thought the 1.50 cm was x1, so we need to find x2. I figured the L,w, and d would all be the same for both cases so I rearranged the equation so that (Lw)/d=x/n. then I set x1/n1=x2/n2 and solved for x2 and got about 2 cm. This was not right. Any help would be greatly appreciated thank you!

 

[anathema]

Hello,

Thank you for sharing your attempt at a solution. Your approach is on the right track, but there are a few things to consider.

First, when light travels from air to water, the wavelength of the light changes. This can be calculated using the equation λ2 = λ1 / n, where λ1 is the original wavelength (632 nm) and n is the refractive index of water (1.33).

Second, the distance between the slits (d) and the distance from the slits to the screen (L) may also change when the tube is filled with water. This is because the water will have a different refractive index than air, which affects the path of the light.

So, to find the separation of the bright spots in water, you will need to use the equation you mentioned (nw)/d=x/L, but with the new values for λ2, d, and L.

I hope this helps! Let me know if you have any other questions or if you need further clarification.