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.

30.4 cm

when the light travels from one medium to another then its speed changes because of refractive index. Due to this it changes its path and bends by small angle. Hence when the observer observes the vessel, the height will be different from the actual height of the vessel.

Shift due to water

Shift due to oil

Total shift Δt = 5 + 4.6 = 9.6 cm

Apparent depth = 40 - (9.6) = 30.4 cm below the surface.