A vessel of depth 2h is half-filled with a li | vedclass

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(B) The apparent depth $(d_{app})$ of an object seen through multiple layers of liquids is given by the sum of the apparent depths of each layer: $d_{

Vedclass · Accepted Answer

$\frac{3}{4} h \sqrt{2}$

Vedclass · Answer

(B) The apparent depth $(d_{app})$ of an object seen through multiple layers of liquids is given by the sum of the apparent depths of each layer: $d_{app} = \sum \frac{h_i}{\mu_i}$.Here, the total depth is $2h$. The lower half has depth $h$ and refractive index $\mu_1 = 2\sqrt{2}$. The upper half has depth $h$ and refractive index $\mu_2 = \sqrt{2}$.The apparent depth of the bottom surface as seen from the top is:$d_{app} = \frac{h_1}{\mu_1} + \frac{h_2}{\mu_2}$$d_{app} = \frac{h}{2\sqrt{2}} + \frac{h}{\sqrt{2}}$$d_{app} = \frac{h + 2h}{2\sqrt{2}} = \frac{3h}{2\sqrt{2}}$Rationalizing the denominator:$d_{app} = \frac{3h 	imes \sqrt{2}}{2\sqrt{2} 	imes \sqrt{2}} = \frac{3\sqrt{2}h}{4} = \frac{3}{4}h\sqrt{2}$.

$A$ vessel of depth $2h$ is half-filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

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