Two light waves having the same wavelength $λ$ in vacuum are in phase initially. Then the first wave travels a path $L_{1}$ through a medium of refractive index $n_{1}$ while the second wave travels a path of length $L_{2}$ through a medium of refractive index $n_{2}$ . After this the phase difference between the two waves is :

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$\frac{2 π}{λ} (\frac{L_{2}}{n_{1}} - \frac{L_{1}}{n_{2}})$

$\frac{2 π}{λ} (n_{2} L_{1} - n_{1} L_{2})$

$\frac{2 π}{λ} (\frac{L_{1}}{n_{1}} - \frac{L_{2}}{n_{2}})$

$\frac{2 π}{λ} (n_{1} L_{1} - n_{2} L_{2})$

answer is A.

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Detailed Solution

Optical path = $μ l$
$∴$ Phase difference = $\frac{2 π}{λ} (Δ x)$
$ϕ = \frac{2 π}{λ} (n_{1} L_{1} - n_{2} L_{2})$

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