Two light ways having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path L1 through a medium of refractive index μ 1 while the second ray travels a path L2 through a medium of refractive index μ 2 . The two waves are then combined to observe interference. The phase difference between the two waves is

Question

Two light ways having the same wavelength in vacuum are in phase initially. Then, the first ray travels a path L1 through a medium of refractive index μ 1 while the second ray travels a path L2 through a medium of refractive index μ 2 . The two waves are then combined to observe interference. The phase difference between the two waves is (A) (2 π /λ )((L1/(μ )1) - (L2/(μ )2)) (B) (2 π /λ )(L2 - L1) (C) (2 π /λ )((μ )2 L1 - (μ )1 L2) (D) (2 π /λ )((μ )1 L1 - (μ )2 L2)

Tardigrade Admin · Accepted Answer

Optical path for first ray =μ 1L1 Optical path for second ray =μ 2L2 So, phase difference is given by Δ φ=(2 π /λ )× path difference =(2 π /λ )× Δ x ⇒ Δ φ=(2 π /λ )((μ )1 L1 - (μ )2 L2)

$\frac{2 π}{λ} (\frac{L _{1}}{( μ ) _{1}} - \frac{L _{2}}{( μ ) _{2}})$

$\frac{2 π}{λ} (L_{2} - L_{1})$

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

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

Optical path for first ray $= μ_{1} L_{1}$
Optical path for second ray $= μ_{2} L_{2}$
So, phase difference is given by
$Δ ϕ = \frac{2 π}{λ} \times$ path difference
$= \frac{2 π}{λ} \times Δ x$
$\Rightarrow Δ ϕ = \frac{2 π}{λ} ((μ)_{1} L_{1} - (μ)_{2} L_{2})$

λ2π​((μ)1​L1​​−(μ)2​L2​​)

λ2π​(L2​−L1​)

λ2π​((μ)2​L1​−(μ)1​L2​)

λ2π​((μ)1​L1​−(μ)2​L2​)

Optical path for first ray =μ1​L1​ Optical path for second ray =μ2​L2​ So, phase difference is given by Δϕ=λ2π​× path difference =λ2π​×Δx ⇒Δϕ=λ2π​((μ)1​L1​−(μ)2​L2​)

$\frac{2 π}{λ} (\frac{L _{1}}{( μ ) _{1}} - \frac{L _{2}}{( μ ) _{2}})$

$\frac{2 π}{λ} (L_{2} - L_{1})$

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

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

Optical path for first ray $= μ_{1} L_{1}$
Optical path for second ray $= μ_{2} L_{2}$
So, phase difference is given by
$Δ ϕ = \frac{2 π}{λ} \times$ path difference
$= \frac{2 π}{λ} \times Δ x$
$\Rightarrow Δ ϕ = \frac{2 π}{λ} ((μ)_{1} L_{1} - (μ)_{2} L_{2})$