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

1. Oct 8, 2012

nishantve1

1. The problem statement, all variables and given/known data

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 ?

2. Relevant 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 dont understand like

3. The attempt at a solution

The solution says : When light travels through a sheet of thickness t, the optical path travelled 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