A vessel of height 2 d is half filled with a liquid of refractive index 2 and the other half with a liquid of refractive index n (the given liquids are immiscible). Then, the apparent depth of the i

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A vessel of height 2 d is half filled with a liquid of refractive index 2 ​ and the other half with a liquid of refractive index n (the given liquids are immiscible). Then, the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

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Refractive index μ = Apparent depth ( x ) Real depth ( d ) ​ For 1st liquid, 2 ​ = x 1 ​ d ​ ⇒ x 1 ​ = 2 ​ d ​ Similarly, for 2nd liquid, n = x 2 ​ d ​ ⇒ x 2 ​ = n d ​ Total apparent depth = x 1 ​ + x 2 ​ = 2 ​ d ​ + n d ​ = n 2 ​ d ( n + 2 ​ ) ​

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