The refractive index of water is $ 1.33 $ and the speed of light in air is $3\times {10}^{8}m{s}^{-1}$. Calculate the speed of light in water.

Given:

Refractive index $(\mu ) \ =  \ 1.33$

Speed of light in air $(c) \ = \ 3\times {10}^{8}m{s}^{-1}$

To find: Speed of light in the water $(v)$.

Solution:

We know that,

$\mu =\frac{c}{v}$

where, $(\mu )$ is the refractive index, $(c)$ is the velocity of light in a vacuum $(3\times {10}^{8}m{s}^{-1})$, $(v)$ is the velocity of light in a substance.

Substituting the given values we get-

$1.33=\frac{3\times {10}^{8}}{v}$

$\frac{133}{100}=\frac{3\times {10}^{8}}{v}$

$v=\frac{3\times {10}^{8}\times 100}{133}$

$v=\frac{300\times {10}^{8}}{133}$

$v=2.25\times {10}^{8}m/s$

Hence, the speed of light in water is 2.25 x 10⁸m/s.

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Updated on: 10-Oct-2022

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