Question

Two light waves having the same wavelength l in vacuum are in phase initially. Then the first ray travels a path of length L₁ through a medium of refractive index m₁. The second ray travels a path of length L₂ through a medium of refractive index m₂. The two waves are then combined to observe interference effects. The phase difference between the two, when they interfere, is –

• A. $\frac{2\pi}{\lambda}$ (L₁ – L₂)
• B. $\frac{2\pi}{\lambda}$ (m₁L₁ – m₂L₂)
• C. $\frac{2\pi}{\lambda}$ (m₂L₁ – m₁L₂)
• D. $\frac { 2 \pi } { \lambda }$ $\left\lbrack \frac{L_{1}}{\mu_{1}} - \frac{L_{2}}{\mu_{2}} \right\rbrack$

Answer 1

Answer: (B)

$\frac{2\pi}{\lambda}$ (m₁L₁ – m₂L₂)

Answer 2

Optical path length through S₁ = m₁L₁

Optical path length through S₂ = m₂L₂

Total path difference D = (m₁L₁ – m₂L₂)

f = $\frac{2\pi}{\lambda}$D $\begin{matrix} \varphi = \frac{2\pi}{\lambda}(\mu_{1}L_{1} - \mu_{2}L_{2}) \end{matrix}$