Question

The apparent depth of an object at the bottom of a tank filled with a liquid of refractive index $1.3$ is $7.7cm$. What is the actual depth of the liquid in the tank?

Answer 1

Step-1: Given

Refractive index of liquid, n = $1.3$

The apparent depth of an object in the liquid, h = $7.7cm$

Real depth of the object, d =?

Step-2: Calculation:

Calculating the real depth of the object,

The formula for reflective index is,

$$\begin{gathered} Refractiveindex,n=\frac{Realdepth\left(d\right)}{Apparentdepth\left(h\right)} \\ \to 1.3=\frac{d}{7.7} \\ \to d=7.7\times 1.3 \\ \Rightarrow d=10.01cm \end{gathered}$$

Hence, the real depth of the object is $10.01cm$.