Question

A beaker $20cm$ high is half filled with an oil of refractive index $1.40$ and the upper half filled with water of refractive index $1.33$. What is the apparent depth of the beaker as observed normally?

Answer 1

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

$\frac{1.33}{1.4}=\frac{10}{x}$

$x=\frac{10\times 1.4}{1.33}$ . . . . . . ( 1 )

from air :

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

1.33 = $\frac{\frac{10+10\times 1.4}{1.33}}{apparentdepth}$

so apparent depth = 2.07 cm