Two light waves having the same wavelength la | vedclass

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Question

(A) The optical path length of a wave traveling through a medium of refractive index $n$ and geometric path length $L$ is given by $OPL = n 	imes L$.

Vedclass · Accepted Answer

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

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(A) The optical path length of a wave traveling through a medium of refractive index $n$ and geometric path length $L$ is given by $OPL = n 	imes L$.The optical path length for the first wave is $OPL_{1} = n_{1}L_{1}$.The optical path length for the second wave is $OPL_{2} = n_{2}L_{2}$.The optical path difference between the two waves is $\Delta p = |OPL_{1} - OPL_{2}| = |n_{1}L_{1} - n_{2}L_{2}|$.The phase difference $\Delta \phi$ is related to the path difference $\Delta p$ by the formula $\Delta \phi = \frac{2 \pi}{\lambda} \Delta p$.Substituting the path difference,we get $\Delta \phi = \frac{2 \pi}{\lambda} (n_{1}L_{1} - n_{2}L_{2})$.

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