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(A) $ 1.94 \times {10^8}m{s^{ - 1}} $

(B) $ 3 \times {10^8}m{s^{ - 1}} $

(C) $ 4.62 \times {10^8}m{s^{ - 1}} $

(D)None of the above

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Formulae Used: $ \mu = c/v $

Where, $ \mu $ is the absolute refractive index of a medium, $ c $ is the speed of light in air and $ v $ is the speed of light in the medium.

Here, $ \mu $ is given to be 1.54.

$ c $ is given to be $ 3 \times {10^8}m{s^{ - 1}} $ .

$ v $ is not known to us.

Now,

$\Rightarrow \mu = c/v $

$ \Rightarrow v = c/\mu $

Then,

Putting in the values of the known terms,

$\Rightarrow v = 3 \times {10^8}m{s^{ - 1}}/1.54 $

By calculating, we get

$\Rightarrow v = 1.94 \times {10^8}m{s^{ - 1}} $

The ratio of absolute refractive index of a medium to the absolute refractive index of another medium.

Let us take

$ {\mu _1} $ to be the absolute refractive index of medium 1 and $ {\mu _2} $ be that of medium 2.

Now,

By definition,

$\Rightarrow {\mu _1} = c/{v_1} $

Similarly,

$\Rightarrow {\mu _2} = c/{v_2} $

Now,

Let us say a beam of light is travelling from medium 1 to medium 2.

So the refractive index of medium 2 relative to medium 1 is given by

$\Rightarrow ^1{\mu _2} = {\mu _{21}} = {\mu _1}/{\mu _2} $

Also,

$\Rightarrow {\mu _1} = c/{v_1} $ , $ {\mu _2} = c/{v_2} $

Thus,

$\Rightarrow ^1{\mu _2} = {\mu _{21}} = (c/{v_1})/(c/{v_2}) $

The value $ c $ gets cancelled out and we get,

$\Rightarrow ^1{\mu _2} = {\mu _{21}} = {\mu _1}/{\mu _2} = {v_2}/{v_1} $ .

Refraction of light takes place as the speed of light changes when it travels from one transparent medium to the other. The value of absolute refractive index signifies the ratio by which the speed of light changes or to be more precise by how much light gets refracted.