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A vessel of depth t is half filled with oil of refractive index μ₁ and the other half is filled with water of refractive index μ₂. The apparent depth of the vessel when viewed from above is

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$\frac{2 t μ_{1} μ_{2}}{(μ_{1} + μ_{2})}$

$\frac{2 t (μ_{1} + μ_{2})}{μ_{1} μ_{2}}$

$\frac{t μ_{1} μ_{2}}{2 (μ_{1} + μ_{2})}$

$\frac{t (μ_{1} + μ_{2})}{2 μ_{1} μ_{2}}$

answer is D.

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Detailed Solution

The apparent depth is given by

$A I = \frac{t_{1}}{μ_{1}} + \frac{t_{2}}{μ_{2}} = \frac{t}{2} (\frac{1}{μ_{1}} + \frac{1}{μ_{2}}) = \frac{t (μ_{1} + μ_{2})}{2 μ_{1} μ_{2}}$

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