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(A) The apparent depth $d_{app}$ of an object seen through multiple layers of transparent media is given by the sum of the apparent depths of each lay

Vedclass · Accepted Answer

$\left( \frac{d}{\mu_1} + \frac{d}{\mu_2} \right)$

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(A) The apparent depth $d_{app}$ of an object seen through multiple layers of transparent media is given by the sum of the apparent depths of each layer.For a layer of real depth $d$ and refractive index $\mu$,the apparent depth is $d' = \frac{d}{\mu}$.Here,we have two layers,each of depth $d$.The first layer (bottom) has refractive index $\mu_1$,so its apparent depth is $d_1 = \frac{d}{\mu_1}$.The second layer (top) has refractive index $\mu_2$,so its apparent depth is $d_2 = \frac{d}{\mu_2}$.The total apparent depth is $d_{app} = d_1 + d_2 = \frac{d}{\mu_1} + \frac{d}{\mu_2} = d \left( \frac{1}{\mu_1} + \frac{1}{\mu_2} \right)$.

$A$ container is filled with a liquid of refractive index $\mu_1$ up to a depth $d$ and another liquid of refractive index $\mu_2$ up to a depth $d$ is poured on top of it. What is the apparent depth of the container when viewed from above?

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