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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.
Solution
Given,
Height of water, dw = 20 cm
Height of oil, dO = 20 cm
The refractive index of the water (μw) = 1.33
The refractive index of oil (μO) = 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.
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