Find the number of fringes that will shift in young's double slit experiment

[nishantve1]

Homework Statement

Monochromatic light of wavelength 600nm is used in a young's 'double slit experiment . One of the slits is covered with a thin transparent layer (1.8 * 10^-9m ) made of a material of refractive index n(1.6). How many fringes will shift due to the introduction of the transparent layer ?

Homework Equations

This question uses the concept of optical Path which is = refractive index * thickness of the medium.
This is actually a solved question but there are somethings i don't understand like

The Attempt at a Solution

The solution says : When light travels through a sheet of thickness t, the optical path traveled is nt . where n is the refractive index of the sheet.When one of the slits is covered by the sheet , air is replaced by the sheet and hence, the optical path changes by (n-1)t(HOW?)
further is says, One fringe shifts when optical path changes by one wavelength . (HOW?)
Thus, the number of fringes shifted due to the introduction is
(n-1)t/λ
that gives the answer 18.
I would really appreciate if someone explains me the terms in bold.
Thanks

 

[anathema]

for your question! Let me break down the solution for you:

1. Optical path: This refers to the distance that light travels through a medium, taking into account the refractive index of that medium. In this case, the optical path is equal to the refractive index (n) of the material multiplied by the thickness (t) of the transparent layer.

2. Change in optical path: When one of the slits is covered by the transparent layer, the light must travel through the layer (with refractive index n) instead of through air (with refractive index 1). This means that the optical path changes from nt (when the slit is uncovered) to n(1)t (when the slit is covered). This is because the light now has to travel through a medium with a different refractive index.

3. One fringe shift: In the double slit experiment, fringes appear when light from the two slits interfere with each other. One fringe shift occurs when the path difference between the two interfering beams changes by one wavelength (λ). In this case, the introduction of the transparent layer causes a change in the optical path, which in turn leads to a change in the path difference between the two beams. Therefore, one fringe will shift.

4. Number of fringes shifted: The number of fringes shifted can be calculated by dividing the change in optical path (n(1)t - nt) by the wavelength (λ). This gives us the number of wavelength shifts, which is equal to the number of fringes shifted. In this case, the change in optical path is (n-1)t (as explained in point 2 above), and the wavelength is given as 600nm. This gives us a total of (n-1)t/λ = (1.6-1)(1.8*10^-9)/600*10^-9 = 18 fringes shifted.

I hope this helps to clarify the solution for you. Let me know if you have any further questions.