A vessel 20 cm deep is half-filled with oil of refractive index 1.37 and the other half is filled with water of refractive index 1.33. Find the apparent depth of the vessel when viewed from above.

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Solution

The formula for apparent depth of the vessel is,

A D = \frac{t_{1}}{μ_{1}} + \frac{t_{2}}{μ_{2}} = \frac{t}{2} (\frac{1}{μ_{1}} + \frac{1}{μ_{2}}) = \frac{t (μ_{1} + μ_{2})}{2 μ_{2} μ_{2}}

where,

Depth of the vessel, t = 20 cm,
Refractive index of oil, μ₁ = 1.37 and
Refractive index of water, μ₂ = 1.33

Substituting for t, μ₁ and μ₂, we get
Apparent depth, AD = 15.37 cm.

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Wave Optics

A vessel 20 cm deep is half-filled with oil of refractive index 1.37 and the other half is filled with water of refractive index 1.33. Find the apparent depth of the vessel when viewed from above.

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