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(A) The relation between real depth $(h)$ and apparent depth $(h')$ is given by $h = \mu h'$,where $\mu$ is the refractive index.In the first case,the

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$\frac{d - b}{d - c - b + a}$

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(A) The relation between real depth $(h)$ and apparent depth $(h')$ is given by $h = \mu h'$,where $\mu$ is the refractive index.In the first case,the real depth of the liquid is $h_1 = \mu(b - a)$,where $(b - a)$ is the apparent depth.In the second case,the real depth of the liquid is $h_2 = \mu(d - c)$,where $(d - c)$ is the apparent depth.The difference in real depth is $\Delta h = h_2 - h_1 = \mu(d - c - b + a)$.This difference in real depth is equal to the thickness of the additional liquid added,which is $\Delta h = d - b$.Equating the two expressions: $\mu(d - c - b + a) = d - b$.Therefore,the refractive index is $\mu = \frac{d - b}{d - c - b + a}$.

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