Two immiscible liquids of refractive indices 8 5 and 3 2 respectively are put in a beaker as shown in the figure. The height of each column is 6 cm . A coin is placed at the bottom of the beaker. For

Question

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6 cm$ . A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $\frac{α}{4} cm$ . The value of $α$ is _______.

TestHub · Accepted Answer

The formula to calculate the apparent height of the coin when seen through the combination of liquids can be written as

$h_{app} = \frac{h_{1}}{μ_{1}} + \frac{h_{2}}{μ_{2}} . . . (1)$

From equation (1), it follows that

$\begin{array}{rcl} h_{app} & = & \frac{6}{3 / 2} + \frac{6}{8 / 5} cm \\ = & 4 + \frac{15}{4} cm \\ = & \frac{31}{4} cm \end{array}$

Hence, $α = 31$ .

Physics - Geometrical Optics Question with Solution | TestHub

Doubts & Discussion