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

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56.5 cm

30.4 cm

28.5 cm

63.2 cm

answer is C.

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Detailed Solution

Shift due to water $Δ t_{w} = [1 - \frac{1}{μ}] d = [1 - \frac{1}{1 .33}] 20 = 5 cm$
Shift due to oil, ${Δt}_{0} = [1 - \frac{1}{13}] 20 = 4 .6 cm$
Total shift $Δt = 5 + 4 .6 = 9 .6 cm$
Apparent depth $= 40 - (9 .6) = 30 .4 cm$ below the surface

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