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Question
The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is 2 × 108ms−1, find the speed of light in (i) air, (ii) water.
Solution
Given: Refractive index of water, nw = 4/3 and Refractive index of glass, ng = 3/2
Speed of light in glass, vg = 2×108 m/s
(i)
`n_g/n_a="v"_a/"v"_g` where, `n_a` = refractive index of air = 1
`"v"_a` = speed of light in air
`therefore "v"_a=n_g/n_axx"v"_g=(3/2)/1xx(2xx10^8)=3xx10^8`m/s
(ii)
`n_g/n_w="v"_w/"v"_g`,where, `"v"_w`= speed of light in water
`therefore"v"_w=n_g/n_wxx"v"_g=(3/2)/(4/3)xx(2xx10^8)=2.25xx10^8` m/s
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