Q. Two light rays having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first ray travel a path $L_{1}$through a medium of refractive index $n_{1}$, while the travel second ray travels a path of length $L_{2}$ through a medium of refractive index $n_{2}$. The two waves are then combined to observe interference. The phase difference the two waves is
A) $\frac{2\pi}{\lambda}\left( L_{2} - L_{1} \right)$
B) $\frac{2\pi}{\lambda}\left( {n_{1}L}_{2} - n_{2}L_{1} \right)$
C) $\frac{2\pi}{\lambda}\left( {n_{2}L}_{1} - n_{1}L_{2} \right)$
D) $\frac{2\pi}{\lambda}\left( \frac{L_{1}}{n_{1}} - \frac{L_{2}}{n_{2}} \right)$
Explanation
(b) Optical path for 1st ray=$n_{1}L_{1}$
Optical path for 2nd ray$= n_{2}L_{2}$
$\therefore$Phase difference, $\phi = \frac{2\pi}{\lambda}\Delta x$
$= \frac{2\pi}{\lambda}\left( n_{1}L_{1} - n_{2}L_{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.