A fish is at a depth d in water of refractive index 4/3. If a transparent slab of refractive index 3/2 and thickness d/2 is placed on the surface of water, then which one of the following is the apparent depth of the fish as observed by an observer in air?
\(13d/12\)
For nearly normal viewing through a stack of transparent layers, the total apparent depth measured from the topmost surface equals the sum of each layer's real thickness divided by its own refractive index. Here water has real depth d and refractive index \(4/3\), and the slab has thickness \(d/2\) and refractive index \(3/2\). So apparent depth \(= \dfrac{d}{4/3} + \dfrac{d/2}{3/2} = \dfrac{3d}{4} + \dfrac{d}{3} = \dfrac{9d+4d}{12} = \dfrac{13d}{12}\). Hence the apparent depth of the fish is \(13d/12\).
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