A vessel holds water up to a height of 20 cm , with an oil layer extending another 20 cm above it. The refractive indices of the water and the oil are 1.33 and 1.30 , respectively. Determine the apparent depth of the vessel when viewed from above.

Step-by-step solution

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 = h₁ ₁ + h₂ ₂ Given values are: h₁ = 20 cm (height of water) ₁ = 1.33 (refractive index of water) h₂ = 20 cm (height of oil) ₂ = 1.30 (refractive index of oil) Substituting the values into the formula: d_ app = 20 1.33 + 20 1.30 d_ app 15.04 cm + 15.38 cm d_ app 30.42 cm Rounding to one decimal place, the apparent depth is 30.4 cm .