A vessel of depth d is half filled with oil o | vedclass

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(A) The apparent depth $d_{app}$ of a medium of real depth $d_i$ and refractive index $n_i$ is given by $d_{app, i} = \frac{d_i}{n_i}$.Here,the vessel

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$\frac{d(n_1+n_2)}{2n_1n_2}$

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(A) The apparent depth $d_{app}$ of a medium of real depth $d_i$ and refractive index $n_i$ is given by $d_{app, i} = \frac{d_i}{n_i}$.Here,the vessel has a total depth $d$. It is divided into two halves,so the real depth of each liquid is $d_1 = d_2 = \frac{d}{2}$.The apparent depth of the oil layer is $d_{app, 1} = \frac{d/2}{n_1} = \frac{d}{2n_1}$.The apparent depth of the water layer is $d_{app, 2} = \frac{d/2}{n_2} = \frac{d}{2n_2}$.The total apparent depth of the vessel is the sum of the apparent depths of the two layers:$d_{app} = d_{app, 1} + d_{app, 2} = \frac{d}{2n_1} + \frac{d}{2n_2}$.Factoring out $\frac{d}{2}$,we get $d_{app} = \frac{d}{2} \left( \frac{1}{n_1} + \frac{1}{n_2} \right)$.Simplifying the expression inside the parentheses,we get $d_{app} = \frac{d}{2} \left( \frac{n_2 + n_1}{n_1 n_2} \right) = \frac{d(n_1 + n_2)}{2n_1 n_2}$.

$A$ vessel of depth $d$ is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above will be

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