The R.I of glass and water w.r.t air are $1.5$ and $4 / 3$ respectively. What is the R.I of glass w.r.t water.

\frac{1}{3 π} (\frac{[R_{2} - R_{1}] [2 R_{1} + R_{2}]}{R_{1} + R_{2}})

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\frac{1}{3 π} (\frac{[R_{2} - R_{1}] [2 R_{1} + R_{2}]}{R_{1} - R_{2}}) a b o v e

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\frac{1}{3 π} (\frac{[R_{2} + R_{1}] [2 R_{1} + R_{2}]}{R_{1} \times R_{2}}) a b o v e

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\frac{1}{3 π} (\frac{[R_{2} \times R_{1}] [2 R_{1} + R_{2}]}{R_{1} - R_{2}}) a b o v e

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Solution

The correct option is A $\frac{1}{3 π} (\frac{[R_{2} - R_{1}] [2 R_{1} + R_{2}]}{R_{1} + R_{2}})$
COM at AOC
$= \frac{4}{3 π} (\frac{R_{2}^{3} - R_{1}^{3}}{R_{2}^{2} - R_{1}^{2}}) [] C O M a t A B C = \frac{2 R^{2}}{π} C O M a t t h i s s y s t e m = \frac{m (\frac{2 R^{2}}{π}) - m \frac{4}{3 π} (\frac{R_{2}^{3} - R_{1}^{3}}{R_{2}^{2} - R_{1}^{2}})}{2 m} = \frac{1}{3 π} (\frac{6 R_{2} (R_{2} + R_{1}) - 4 (R_{2}^{2} + R_{1}^{2} + R_{1} R_{2})}{R_{2} + R_{1}}) = \frac{1}{3 π} (\frac{[R_{2} - R_{1}] [2 R_{1} + R_{2}]}{R_{1} + R_{2}}) a b o v e$

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