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Question

How is the refractive index of water related to the real depth and the apparent depth of a column of water ?

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Solution

Let us table a tank full of water having a depth of d and it appears to be at a depth i.e a is apparent depth.
μw is refractive index of water so now from snells law
μwsini=sinr
μw=sinrsini and for small angle; sinθ=θ=tanθ
hence, μw=tanrtani
tanr=Aa,tani=Ad
hence μw=da= real depthapparent depth

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