Question:
Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $h/3$. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.
Three immiscible liquids of densities $d_1 > d_2 > d_3$ and refractive indices $\mu_1 > \mu_2 > \mu_3$ are put in a beaker. The height of each liquid column is $h/3$. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.
Updated On: Feb 22, 2024
- $\frac{h}{6}\left(\frac{1}{\mu_{1}} +\frac{1}{\mu_{2}}+\frac{1}{\mu_{3}}\right)$
- $\frac{h}{6}\left(\frac{1}{\mu_{1}} -\frac{1}{\mu_{2}} - \frac{1}{\mu_{3}}\right)$
- $\frac{h}{3}\left(\frac{1}{\mu_{1}} -\frac{1}{\mu_{2}} - \frac{1}{\mu_{3}}\right)$
- $\frac{h}{3}\left(\frac{1}{\mu_{1}} +\frac{1}{\mu_{2}}+\frac{1}{\mu_{3}}\right)$
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The Correct Option is D
Solution and Explanation
Apparent depth of the dot
$= \frac{h}{3\mu_{1}}+\frac{h}{3\mu_{2}}+\frac{h}{3\mu_{3}} $
$= \frac{h}{3}\left[\frac{1}{\mu_{1}}+\frac{1}{\mu_{2}}+\frac{1}{\mu_{3}}\right]$
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.