# The refractive index of water with respect to vacuum is 4/3 and refractive index of vacuum with respect to glass is .

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The refractive index of water with respect to vacuum is $\frac43$and refractive index of vacuum with respect to glass is $\frac23$. If the speed the speed of light in glass is 2 × 108 ms-1 , find the speed of light in (i) vacuum, (ii) water.

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Given;

Refractive index of (R.I) water w.r.t vacuum = $\frac43$

Refractive index (R.I) of vacuum w.r.t glass = $\frac23$

Refractive index (R.I) of glass to vacuum will be = $\frac32$

Refractive index of glass to water = $\frac{R.I\,of\,glass}{R.I\,of\,water}= \frac{\frac32}{\frac43}$

⇒ Refractive index of glass w.r.t water = $\frac{3\times3}{4\times2}= \frac98$

⇒ $\frac{speed\,of\,light\,in\,water}{speed\,of\,light\,in\,glass}= \frac98$

⇒ $\frac{speed\,of\,light\,in\,water}{2\times10^8}= \frac98$

⇒ Speed of light in water = $\frac{9\times2\times10^8}{8}$

⇒ Speed of light in water = $\frac{9\times10^8}{4}$ = 2.25 x 108

Thus, speed of light in water = 2.25 × 108

Refractive index of water w.r.t vacuum = vμw = $\frac43$

⇒ $\frac{speed\,of\,light\,in\,vacuum}{speed\,of\,light\,in\,water}= \frac43$

⇒ $\frac{speed\,of\,light\,in\,vacuum}{2.25\times10^8}= \frac43$

⇒ Speed of light in water = $\frac{4\times2.25\times10^8}{3}$

⇒ Speed of light in water = $\frac{9\times10^8}{3}$

Thus, speed of light in vacuum is 3 × 108 m/s.

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