Two light waves having the same wavelength λ in vacuum are in phase initially. Then the first ray travels a path of length L1 through a medium of refractive index μ1. The second ray travels a path of length L2 through a medium of refractive index μ2 . The two waves are then combined to observe interference effects. The phase difference between the two, when they interfere, is

Question

Two light waves having the same wavelength λ in vacuum are in phase initially. Then the first ray travels a path of length L1 through a medium of refractive index μ1. The second ray travels a path of length L2 through a medium of refractive index μ2 . The two waves are then combined to observe interference effects. The phase difference between the two, when they interfere, is (A) (2 π/λ)(L1-L2) (B) (2 π/λ)(μ1 L1-μ2 L2) (C) (2 π/λ)(μ2 L1-μ1 L2) (D) (2 π/λ)[(L1/μ1)-(L2/μ2)]

Tardigrade Admin · Accepted Answer

Optical path difference or =μ1 (path) 1-μ2 (path) 2 =(μ1 L1-μ2 L2) ⇒ δ=(2 π/λ) Δ x=(2 π/λ)(μ1 L1-μ2 L2)

$\frac{2 π}{λ} (L_{1} - L_{2})$

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

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

$\frac{2 π}{λ} [\frac{L _{1}}{μ _{1}} - \frac{L _{2}}{μ _{2}}]$

Optical path difference or $= μ_{1}$ (path) $_{1} - μ_{2}$ (path) $_{2}$
$= (μ_{1} L_{1} - μ_{2} L_{2})$
$\Rightarrow δ = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} (μ_{1} L_{1} - μ_{2} L_{2})$

λ2π​(L1​−L2​)

λ2π​(μ1​L1​−μ2​L2​)

λ2π​(μ2​L1​−μ1​L2​)

λ2π​[μ1​L1​​−μ2​L2​​]

Optical path difference or =μ1​ (path) 1​−μ2​ (path) 2​ =(μ1​L1​−μ2​L2​) ⇒δ=λ2π​Δx=λ2π​(μ1​L1​−μ2​L2​)

$\frac{2 π}{λ} (L_{1} - L_{2})$

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

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

$\frac{2 π}{λ} [\frac{L _{1}}{μ _{1}} - \frac{L _{2}}{μ _{2}}]$

Optical path difference or $= μ_{1}$ (path) $_{1} - μ_{2}$ (path) $_{2}$
$= (μ_{1} L_{1} - μ_{2} L_{2})$
$\Rightarrow δ = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} (μ_{1} L_{1} - μ_{2} L_{2})$