Three immiscible transparent liquids with uniform refractive indices 2 3 , 3 4 and 5 6 are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The appa

Question

Three immiscible transparent liquids with uniform refractive indices 2 3 ​ , 3 4 ​ and 5 6 ​ are arranged one on top of another. The depths of the liquids are 3 cm 4 cm and 6 cm respectively. The apparent depth of the vessel is

TestHub · Accepted Answer

The apparent depth of a vessel containing multiple immiscible liquids is given by the sum of the apparent depths of the individual liquid layers.

Apparent depth $D_{a pp} = \frac{d _{1}}{μ _{1}} + \frac{d _{2}}{μ _{2}} + \frac{d _{3}}{μ _{3}}$

Substituting the given values:

$D_{a pp} = \frac{3}{\frac{3}{2}} + \frac{4}{\frac{4}{3}} + \frac{6}{\frac{6}{5}}$

$D_{a pp} = (3 \times \frac{2}{3}) + (4 \times \frac{3}{4}) + (6 \times \frac{5}{6})$

$D_{a pp} = 2 + 3 + 5 = 10$ cm

Answer: 10 cm

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