Two light waves having the same wavelength

Question:

Two light waves having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first wave travels a path $L_{1}$ through a medium of refractive index $\mathrm{n}_{1}$ while the second wave travels a path of length $\mathrm{L}_{2}$ through a medium of refractive index $\mathrm{n}_{2}$. After this the phase difference between the two waves is:

  1. $\frac{2 \pi}{\lambda}\left(\mathrm{n}_{1} \mathrm{~L}_{1}-\mathrm{n}_{2} \mathrm{~L}_{2}\right)$

  2. $\frac{2 \pi}{\lambda}\left(\frac{L_{2}}{n_{1}}-\frac{L_{1}}{n_{2}}\right)$

  3. $\frac{2 \pi}{\lambda}\left(\frac{\mathrm{L}_{1}}{\mathrm{n}_{1}}-\frac{\mathrm{L}_{2}}{\mathrm{n}_{2}}\right)$

  4. $\frac{2 \pi}{\lambda}\left(\mathrm{n}_{2} \mathrm{~L}_{1}-\mathrm{n}_{1} \mathrm{~L}_{2}\right)$

Correct Option: 1

Solution:

$\Delta \mathrm{p}=\mathrm{n}_{1} \mathrm{~L}_{1}-\mathrm{n}_{2} \mathrm{~L}_{2}$

$\Delta \phi=\frac{2 \pi}{\lambda} \Delta \mathrm{p}$

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