A vessel holds water up to a height of 20 cm , with an oil layer...

The apparent depth of a vessel with multiple immiscible liquid layers is given by the sum of the apparent depths of the individual layers.

$d_{app} = \dfrac{h_1}{\mu_1} + \dfrac{h_2}{\mu_2}$

Given values are:
$h_1 = 20 \text{ cm}$ (height of water)
$\mu_1 = 1.33$ (refractive index of water)
$h_2 = 20 \text{ cm}$ (height of oil)
$\mu_2 = 1.30$ (refractive index of oil)

Substituting the values into the formula:

$d_{app} = \dfrac{20}{1.33} + \dfrac{20}{1.30}$

$d_{app} \approx 15.04 \text{ cm} + 15.38 \text{ cm}$

$d_{app} \approx 30.42 \text{ cm}$

Rounding to one decimal place, the apparent depth is $30.4 \text{ cm}$.