Question

What is the speed of light in Quartz having a refractive index of 1.54 if its speed in air is $3 \times {10^8}m{s^{ - 1}}$ ?
(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

Answer 1

Hint : We will use the concept that the absolute refractive index of a medium is the ratio of speed of light in air to the speed of light in the medium. Then we will equate the values and come up with a solution.

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.

Complete step by step answer
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
$\Rightarrow v = 1.94 \times {10^8}m{s^{ - 1}}$
Hence, the correct option is (A).

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

Note
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.