Question

In double slit experiment fringes are obtained using light of wavelength $4800A^o$. 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 $8\times {10}^{-3}mm$

Change in path difference due to first glass film =$t\left({\mu }_{1}1\right)$

Change in path difference due to second glass film =$t({\mu }_2-1)$

Overall change in path difference =$t({\mu }_2-{\mu }_1)$

Path difference between central fringe and 5th bright fringe= $5\lambda$ =$t({\mu }_2-{\mu }_1)$

Hence, $t=\frac{5\lambda }{1.7-1.4}=8\times {10}^{-3}mm$