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Young's double-slit experiment is performed using light of wavelength $λ$ . A thin glass plate of refractive index 1.5 and thickness t is now introduced in the path of one of the interfering beams. The value of t so that the central bright fringe is replaced by its neighboring dark fringe is $nλ$ . The value of n is:

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Detailed Solution

Path difference for first dark fringe from central maxima, $x_{1} = \frac{λ}{2}$

Path difference caused by the thin film used across any one slit,

$x_{2} = (μ - 1) t$

According to the question,
$x_{1} = x_{2} \Rightarrow (μ - 1) t = \frac{λ}{2}$
$\Rightarrow t = \frac{λ}{2 (μ - 1)} \Rightarrow t = \frac{λ}{2 (1.5 - 1)} = λ$

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