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

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

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

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

answer is C.

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Detailed Solution

$λ n_{1} = \frac{λ}{n_{1}} λ n_{2} = \frac{λ}{n_{2}} {(Δ ϕ)}_{1} = \frac{2 π}{λ n_{1}} L_{1} {(Δ ϕ)}_{2} = \frac{2 π}{λ n_{2}} L_{2} Δ ϕ_{1} - Δ ϕ_{2} = \frac{2 π}{λ} (n_{1} L_{1} - n_{2} L_{2}) O p t i c a l p a t h Δ x_{1} = n_{1} L_{1} Δ x_{2} = n_{2} L_{2}$