Question

A monochromatic beam of light of wavelength $5000\mathring{A}$ is used in young's double slit experiment. If one of the slits is covered by a transparent sheet of thickness $1.4\times {10}^{-5}m$, having refractive index of its medium $1.25$. Then the number of fringes shifted is

Answer 1

When light travels through a sheet of thickness t, the optical path travelled is $\mu t$, where $\mu$ 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 $(\mu -1)t$.

One fringe shifts when optical path changes by one wavelength.
Hence $n\lambda =t(\mu -1)$
where n is the number of shifted fringes.

Hence $n=\frac{t(\mu -1)}{\lambda }=7$