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A layer of oil 3 cm thick is floating on a layer of coloured water 5 cm thick. The refractive index of the coloured water is $5/3cm$ and the apparent shift of the two liquids is $20/7 cm$ . Then refractive index of the oil is

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Detailed Solution

t_{oil} = 3 cm; μ_{oil} = ?

$t_{w} = 5 cm; μ_{w} = \frac{5}{3}$

$Total shift = \frac{20}{7}$

$\frac{20}{7} = t_{oil} (1 - \frac{1}{μ_{o i l}}) + t_{w} (1 - \frac{1}{μ_{w}})$

$\frac{20}{7} = 3 (1 - \frac{1}{μ}) + 5 (1 - \frac{1}{\frac{5}{3}})$

$\frac{20}{7} = 3 - \frac{3}{μ} + 2$

$\frac{20}{7} = 5 - \frac{3}{μ}$

$\frac{20}{7} - 5 = - \frac{3}{μ}$

$\frac{20 - 35}{7} = - \frac{3}{μ}$

$\frac{- 15}{7} = \frac{- 3}{μ}$

$μ = \frac{7}{5}$

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