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A vessel of depth 2d cm is half filled w...

A vessel of depth 2d cm is half filled with a liquid of refractive index `mu_(1)` and the upper half with a liquid of refractive index `mu_(2)`. The apparent depth of the vessel seen perpendicularly is

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Let us consider a thin layer of thickness dy at a depth of y.
Apparent thickness of this elementary layer(dH.) = `(dy)/mu , =(dy)/(1+ y/H)`
`:.` Apparent depth (H.) = `int_(0)^(H)(dH.)`
= `int_(0)^(H)((dy)/(1+y/H))` = H ln2
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