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# A Plastic film of thickness t is placed in the path of one of the interfering wave in the young's double slit experiment and it is found that the central fringe is displaced through a width of 5 fringes . If wavelength of light used is $5890 A^{\circ}$ What is thickness of film used

$(a)\;6.45 \times 10^{-4}\;m \\ (b)\;6.05 \times 10^{-4}\;m \\ (c)\;5.20 \times 10^{-4}\;m \\ (d)\;2.35 \times 10^{-4}\;m$

$X_0 =\large\frac{ \beta (\mu-1)t}{\lambda}$
Shift $= 5 \beta$
$5 \beta =\large\frac{ \beta (1.45 -1)t}{5890 \times 10^{-10}}t$
Solving,
$\therefore t= 6.54 \times 10^{-4}$
Hence a is the correct answer.

edited Jul 15, 2014