Question

Fringes are produced by monochromatic light of wavelength $5450\, \mathring{A}$. A thin plate of glass of refractive index $1.5$ is then placed normally in the path of one of the interfering beams and the central bright band of the fringe system is found to move into the position previously occupied by the third band from the centre. The thickness of the glass is found to be $N \times 10^{-6} m$. The value of $N$ is________.

Answer 1

Path difference (when a material of refractive index $\mu$ is placed in path of light),
$x _{0}=\frac{(\mu-1) t \beta}{\lambda}$
Here $x_{0}=3 \beta$
$\therefore 3 \beta =\frac{(\mu-1) t \beta}{\lambda}$
or $t =\frac{3 \lambda}{\mu-1}=\frac{3 \times 5450 \times 10^{-10}}{1.5-1}$
$=3.27 \times 10^{-6} m$