Question

A coherent light of wavelength lambda is falling on a screen with two thin slits, producting an interference pattern on a viewing screen far away from the slits. A thin film of plastic with index of refraction n is used to cover one slit, and the whole interference pattern shifts. The central maximum (m = 0) moves to the side, and what used to be the seventh maximum (m = 7) now occupies its place at the center of the viewing screen. What is the thickness of the film?

Answer 1

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

One fringe shifts when optical path changes by one wavelength .

Thus, the number of fringes shifted due to the introduction is7

so 7= (n-1)t/λ

so, t = 7 $\lambda$ /(n-1)