A vessel of height 2d is half-filled with a l | vedclass

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(B) The apparent depth of an object in a medium is given by the formula: $	ext{Apparent depth} = \frac{	ext{Real depth}}{	ext{Refractive index}}$.T

Vedclass · Accepted Answer

$\frac{d(n+\sqrt{2})}{n \sqrt{2}}$

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(B) The apparent depth of an object in a medium is given by the formula: $	ext{Apparent depth} = \frac{	ext{Real depth}}{	ext{Refractive index}}$.The vessel has a total height of $2d$. It is half-filled with two immiscible liquids,so the real depth of each liquid is $d$.For the first liquid with refractive index $\mu_1 = \sqrt{2}$,the apparent depth $x_1$ is:$x_1 = \frac{d}{\sqrt{2}}$For the second liquid with refractive index $\mu_2 = n$,the apparent depth $x_2$ is:$x_2 = \frac{d}{n}$The total apparent depth of the bottom of the vessel is the sum of the apparent depths of the two layers:$	ext{Total apparent depth} = x_1 + x_2 = \frac{d}{\sqrt{2}} + \frac{d}{n}$Taking the common denominator:$	ext{Total apparent depth} = \frac{dn + d\sqrt{2}}{n\sqrt{2}} = \frac{d(n + \sqrt{2})}{n\sqrt{2}}$

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