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A thin transparent plate of thickness $t$ and refractive index $\mu$ is introduced in the path of one of the two interfering waves. The path difference between these waves is changed by half the wavelength of light $\lambda$. The thickness of the plate is
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The correct answer is:
$\frac{\lambda}{2(\mu-1)}$
Path difference after passing through a plate of thickness $t$ and refractive index $\mu$ is given by,
$\Delta x=(\mu-1) t=\frac{\lambda}{2}$
$\therefore t=\frac{\lambda}{2(\mu-1)}$
$\Delta x=(\mu-1) t=\frac{\lambda}{2}$
$\therefore t=\frac{\lambda}{2(\mu-1)}$
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