Question

A tissue with a refractive index 1.33 is introduced in one of the light paths of a Michelson interferometer operating with a monochromatic coherent light source of wavelength $589\text{nm}$. After the introduction of a tissue sample of thickness $\Delta t$. the fringe pattern is observed to shift by 50 fringes. If thickness is 2 $\Delta t$, the fringe pattern will shift by

• A. 25 fringes
• B. 50 fringes
• C. 200 fringes
• D. 100 fringes

Answer 1

The correct option is D 100 fringes

$n\lambda =2\Delta x=2t(\mu -1)[\therefore n\propto t]$
as $\Delta t$ is replaced to $2\left(\Delta t\right)$
$\therefore n$ will also gets doubled
$n^{{}^{\prime }}=2n=2\times 50=100\text{fringes}$