Question

In double slit experiment fringes are obtained using light of wavelength $4800$ A${}^{\circ }$. One slit is covered with a thin glass film of refractive index $1.4$ and another slit is covered by a film of same thickness but refractive index $1.7$. By doing so the central fringe is shifted to fifth bright fringe in the original pattern. The thickness of glass film is :

• A. $2\times {10}^{-3}$ mm
• B. $4\times {10}^{-3}$ mm
• C. $6\times {10}^{-3}$ mm
• D. $8\times {10}^{-3}$ mm

Answer 1

The correct option is D $8\times {10}^{-3}$ mm

$5^{th}brightfringe=\frac{5\lambda D}{d}$
So, $\Delta y=\frac{5\lambda D}{d}$
and $\Delta y=\frac{D}{d}({\mu }_2-{\mu }_1)twhere,{\mu }_{1}and{\mu }_2$ are refratice index of film introduced.
so, $\frac{5\lambda D}{d}=\frac{D}{d}(1.7-1.4)t$
$t=\frac{5\lambda }{0.3}$
$=\frac{5\times 4800\times {10}^{-10}}{0.3}$
$=8\times {10}^{-6}m$
$=8\times {10}^{-3}mm.$