A vessel of total depth d is half-filled with oil of refractive index n₁ and half-filled with water of refractive index n₂. Viewed normally from above, its apparent depth is:
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Question

A vessel of total depth d is half-filled with oil of refractive index n₁ and half-filled with water of refractive index n₂. Viewed normally from above, its apparent depth is:

G1 Physics · Accepted Answer

The upper layer has thickness d/2 and refractive index n₁, while the lower layer has thickness d/2 and refractive index n₂. For normal viewing through plane layers, apparent thicknesses add: dₐₚₚ = (d/2)/n₁ + (d/2)/n₂ = d/2 [1/n₁ + 1/n₂] = d(n₁+n₂)/(2n₁n₂) Hence option A follows.