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Question

(C) The optical path length $(OPL)$ is defined as the product of the refractive index $(\mu)$ and the geometric distance $(d)$ traveled in that medium

Vedclass · Accepted Answer

$\frac{\pi}{2}$

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(C) The optical path length $(OPL)$ is defined as the product of the refractive index $(\mu)$ and the geometric distance $(d)$ traveled in that medium. The total optical path length between points $P$ and $Q$ is the sum of the optical path lengths in each medium:$OPL = \mu_1 d_1 + \mu_2 d_2 + \mu_3 d_3$Given $\mu = 1$,the refractive indices are $1, 2, 3$ and the distances are $2.25\lambda_0, 3.5\lambda_0, 3\lambda_0$ respectively.$OPL = (1 	imes 2.25\lambda_0) + (2 	imes 3.5\lambda_0) + (3 	imes 3\lambda_0)$$OPL = 2.25\lambda_0 + 7\lambda_0 + 9\lambda_0 = 18.25\lambda_0$The phase difference $\Delta \phi$ is related to the optical path difference $\Delta x$ by the formula $\Delta \phi = \frac{2\pi}{\lambda_0} 	imes \Delta x$.$\Delta \phi = \frac{2\pi}{\lambda_0} 	imes 18.25\lambda_0 = 36.5\pi$Since $36.5\pi = 36\pi + 0.5\pi$,the effective phase difference is $0.5\pi = \frac{\pi}{2}$.

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