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Refractive index of glass with respect to water is $\frac{5}{4}$ and the refractive index of water with respect to air is $\frac{4}{3}$ , what is the refractive index of glass with respect to air?

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\frac{5}{3}

\frac{5}{4}

\frac{16}{15}

1.5

answer is A.

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Detailed Solution

The refractive index of water with respect to air is

\frac{5}{3}

Given information:
The refractive index of glass with respect to water

R_{gw}

\frac{5}{4}

.
The refractive index of glass with respect to air is

R_{ga}

\frac{4}{3}

To find the refractive index of water with respect to air

R_{wa}

The refractive index of glass with respect to water is

R_{gw} = \frac{R_{g}}{R_{W}} - - - - - (1)

put the value in the above equation

(1)

\frac{5}{4} = \frac{R_{g}}{R_{W}}

again the refractive index of glass with respect to air is

R_{ga} = \frac{R_{g}}{R_{a}} - - - - - (2)

put the value in the above equation

(2)

\frac{4}{3} = \frac{R_{g}}{R_{a}}

So the refractive index of water with respect to air is

R_{wa} = \frac{R_{ga}}{R_{gw}}

{\Rightarrow R}_{wa} = \frac{\frac{R_{g}}{R_{a}}}{\frac{R_{g}}{R_{W}}}

{\Rightarrow R}_{wa} = \frac{\frac{4}{3}}{\frac{5}{4}}

{\Rightarrow R}_{wa} = \frac{\frac{4}{3}}{\frac{5}{4}}

{\Rightarrow R}_{wa} = \frac{5}{3}

Hence, the refractive index of water with respect to air is

\frac{5}{3}

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