Question

A jar contains two immiscible liquids A and B with a coin at its bottom. The depths of liquid A and liquid B are $6cm$ and $8cm$ respectively. If the apparent depth of the coin is $9cm$ and refractive index of liquid A is $1.5$, what is the refractive index of liquid B ?

Answer 1

Consider the refrective index,

$\mu =\frac{realdepth}{apparentdepth}$

The apparent deph for liquid $A$ is:

$\frac{realdepth}{refractiveindex}=\frac{6}{1.5}$

The apparent deph for liquid $B$ is:

$\frac{realdepth}{refractiveindex}=\frac{8}{x}$

Therefore the total apparent depth is:

$\begin{array}{c}\frac{6}{1.5}+\frac{8}{x}=9\\ \Rightarrow \frac{6x+12}{1.5x}=9\\ \Rightarrow 6x+12=13.5x\\ \Rightarrow 7.5x=12\\ \Rightarrow x=\frac{12}{7.5}=1.6\end{array}$