The water’s refractive index with respect to vacuum is $\frac{4}{3}$ and refractive index of vacuum with respect to glass is $\frac{2}{3}$ , if the speed of light in glass is $2 \times 10^{8} m / s$ , the speed of light in vacuum is ____ $\times 10^{8} m / s$ .

Question

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If water’s refractive index with respect to vacuum is

\frac{4}{3}

and refractive index of vacuum with respect to glass is

\frac{2}{3}

, if the light’s speed in glass is

2 \times 10^{8} m / s

then the light’s speed in vacuum is

3 \times 10^{8} m / s

.
It is given that the water’s refractive index with respect to vacuum

n_{vw} = \frac{4}{3}

, refractive index of vacuum with respect to glass

n_{gv} = \frac{2}{3}

and the speed of light in glass is

2 \times 10^{8} m / s

.
Since, refractive index of vacuum with respect to glass is

n_{gv} = \frac{2}{3}

, the refractive index of glass with respect to vacuum is

n_{vg} = \frac{1}{n_{gv}}

\Rightarrow n_{vg} = \frac{3}{2}

Since, speed of light in medium is given as

v = \frac{c}{n}

Where

v

is the speed light in medium,

c

is the speed of light in air and

n

is the refractive index.
It can be written as

v_{g} = \frac{c}{n_{vg}}

On substituting the given values, we get the speed of light as

c = {n_{vg} \times v}_{g}

\Rightarrow c = \frac{3}{2} \times 2 \times 10^{8}

\Rightarrow c = 3 \times 10^{8} m / s

Hence, light’s speed in vacuum is

3 \times 10^{8} m / s

.

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