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  4. A vessel is quarter filled with a liquid of refractive index μ. The remaining part of the vessel is filled with an immiscible liquid of refractive index 1.5 μ. The apparent depth of the vessel is 50 % of the actual depth. The value of μ is

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Q. A vessel is quarter filled with a liquid of refractive index $\mu$. The remaining part of the vessel is filled with an immiscible liquid of refractive index $1.5\, \mu$. The apparent depth of the vessel is $50 \%$ of the actual depth. The value of $\mu$ is

Ray Optics and Optical Instruments

Solution:

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$S=\text { Shift }=\frac{3 h}{4}\left(1-\frac{2}{3 \mu}\right)+\frac{h}{4}\left(1-\frac{1}{\mu}\right)=\frac{h}{2}$
Solving above equation, $\mu=\frac{3}{2}$