Question

What is the speed of light in water given that the refractive index of water is 1.31?

Answer 1

Refractive index = Speed of light in vaccum / Speed of light in water.

. It is denotes as n = c / v, v = c / n= 3 × 10^8 m/s / (1.31) =  229 007 634 m/s.

Therefore, refractive index of the water can be measure by the Speed of light in water is  229 007 634 m/s.

Answer 2

ANSWER

$2.29\times 10^{8}$m/s

Step By Step Explanation

As we know that >

The speed of light in Vaccum or air=$3 \times 10^{8}$m/s

The speed of light in the medium i.e water(here) =?

Refractive index of water =1.31

Now, we know that =>

$Refractive \: index \: of \: a \: medium = \dfrac{Speed \: of \: light \: in \: vacuum}{Speed \: of \: light \: in \: medium}$

It can be represented by >>

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

where $\mu = Refractive \: index \: of \: medium$

c = speed of light in air or vacuum

v = Speed of light in medium.

So we get >

$1.31 = \dfrac{3\times10^{8} }{v}$

$\implies v = \dfrac {3\times10^{8} }{1.31}$

$\implies v = 2.29 \times 10^{8}$m/s

Hence the speed of light in water is $2.29\times 10^{8}$m/s.

Remember

-Refractive index has no units as it is the ratio of speed if the light in vacuum to that of light in a medium.

$- Refractive \: index \: of \: a \: medium = \dfrac{Speed \: of \: light \: in \: vacuum}{Speed \: of \: light \: in \: medium}$