Question

A vessel contains water up to a height of 20 cm and above it an oil up to another 20 cm. The refractive indices of the water and the oil are 1.33 and 1.30 respectively. Find the apparent depth of the vessel when viewed from above.

Answer 1

Given,
Height of water, d_w = 20 cm
Height of oil, d_O = 20 cm
The refractive index of the water (μ_w)  = 1.33
The refractive index of oil (μ_O)  = 1.30

Shift due to water is given by,
\[∆  t_w  = 1 - \left( \frac{1}{\mu_w} \right) d_w\] 
\[= \left[ 1 - \left( \frac{1}{1 . 33} \right) \right]20\]

\[= \frac{1}{4}\left( 20 \right) = 5  cm\] 
Shift due to oil,

\[∆  t_O  = \left[ 1 - \left( \frac{1}{1 . 3} \right) \right]20\] 

\[ = 4 . 6  \text{ cm }\]

Therefore, total shift, Δt = 5 + 4.6 = 9.6 cm
Hence, apparent depth = 40 − (9.6) = 30.4 cm between the surface.