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

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(A) The apparent depth of an object in a medium is given by $d' = \frac{d}{\mu}$,where $d$ is the real depth and $\mu$ is the refractive index.Here,th

Vedclass · Accepted Answer

$\frac{x(\mu_1 + \mu_2)}{2\mu_1\mu_2}$

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(A) The apparent depth of an object in a medium is given by $d' = \frac{d}{\mu}$,where $d$ is the real depth and $\mu$ is the refractive index.Here,the vessel of total depth $x$ is divided into two layers of depth $\frac{x}{2}$ each.The first layer is oil with refractive index $\mu_1$,so its apparent depth is $d_1 = \frac{x/2}{\mu_1} = \frac{x}{2\mu_1}$.The second layer is water with refractive index $\mu_2$,so its apparent depth is $d_2 = \frac{x/2}{\mu_2} = \frac{x}{2\mu_2}$.The total apparent depth is the sum of the apparent depths of the two layers:$d_{total} = d_1 + d_2 = \frac{x}{2\mu_1} + \frac{x}{2\mu_2} = \frac{x}{2} \left( \frac{1}{\mu_1} + \frac{1}{\mu_2} \right) = \frac{x}{2} \left( \frac{\mu_1 + \mu_2}{\mu_1\mu_2} \right) = \frac{x(\mu_1 + \mu_2)}{2\mu_1\mu_2}$.

$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is

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