Question

A double-slit apparatus is immersed in a liquid of refractive index $1.33$. It has a slit separation of $1mm$ and distance between the plane of slits and screen $1.33m$. The slits are illuminated by a parallel beam of light whose wavelength in air is $800nm$
(i) Calculate the fringe width
(ii) One of the slits of the apparatus is covered by a thin glass sheet of refractive index $1.53$. Find the smallest thickness of the sheet to bring the adjacent minima on the axis.

Answer 1

(a) $\beta =\frac{\lambda D}{d}$

$\beta =\frac{6300\times 1.33\times {10}^{-10}}{1.33\times 1\times {10}^{-3}}$

$=6.3\times {10}^{-4}m$

(b) Path diff. $\Delta x$

$\Delta x=\left(\frac{a{\mu }_z}{a{\mu }_2}-1\right)t$

$\Delta x=0.15t$

Max. at o on axis should be shifted to bring adjacent minima __.

$\Delta x=\frac{{\lambda }_2}{2}$ or $0.15t=\frac{{\lambda }_a}{2\mu }$

$0.15t=\frac{6300\times {10}^{-10}}{2\times 1.33}$

$t=1.575\times {10}^{-6}m$