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If the absolute refractive index of glass and water are 3/2 and 4/3 respectively, what is the refractive index of glass with respect to water?
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Solution
If v_{1} is the velocity of light in vacuum, v_{2} is the velocity of light in glass and v_{3} is the velocity of light in water then, absolute refractive index of glass, i.e., a refractive index of glass with respect to vacuum,
`"n"_"g" = "v"_1/"v"_2 = 3/2` ...(i)
Absolute refractive index of water ,i.e., refractive index of water with respect to vacuum,
`"n"_"w" = "v"_1/"v"_3 = 4/3` ...(ii)
∴ Refractive index of glass with respect to water,
_{g}n_{w} = `"v"_3/"v"_2`
`= "v"_1/"v"_2 xx "v"_3/"v"_1` ....(Multiplying and dividing R.H.S. of equation by v_{1})
`= 3/2 xx 3/4` ...[From equations (i) and (ii)]
`= 9/8`
The refractive index of glass with respect to water is `9/8`
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