Question

Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first ray travels a path of length $L_{1}$ through a medium of refractive index $\mu_{1}$. The second ray travels a path of length $L_{2}$ through a medium of refractive index $\mu_{2} .$ The two waves are then combined to observe interference effects. The phase difference between the two, when they interfere, is

• A. $\frac{2 \pi}{\lambda}\left(L_{1}-L_{2}\right)$
• B. $\frac{2 \pi}{\lambda}\left(\mu_{1} L_{1}-\mu_{2} L_{2}\right)$
• C. $\frac{2 \pi}{\lambda}\left(\mu_{2} L_{1}-\mu_{1} L_{2}\right)$
• D. $\frac{2 \pi}{\lambda}\left[\frac{L_{1}}{\mu_{1}}-\frac{L_{2}}{\mu_{2}}\right]$

Answer 1

Answer: (B)

Optical path difference or $=\mu_{1}$ (path) $_{1}-\mu_{2}$ (path) $_{2}$
$=\left(\mu_{1} L_{1}-\mu_{2} L_{2}\right)$
$\Rightarrow \delta=\frac{2 \pi}{\lambda} \Delta x=\frac{2 \pi}{\lambda}\left(\mu_{1} L_{1}-\mu_{2} L_{2}\right)$