Question

The refractive index of water is 1.33. What will be the speed of light in water?
A. $3 \times {10^8}\,m.{s^{ - 1}}$
B. $2.25 \times {10^8}\,m.{s^{ - 1}}$
C. $4 \times {10^8}\,m.{s^{ - 1}}$
D. $1.33 \times {10^8}\,m.{s^{ - 1}}$

Answer 1

In order to answer this question, first we will rewrite the given value of refractive index with its symbol and then to find the speed of light in water, we will apply the formula of refractive index in terms of speed of light in both vacuum and water. As we already know the value of speed of light in the vacuum.

Complete step by step answer:
Given: Refractive index of water, $n = 1.33$. The rate of change of refractive index with respect to distance in the material is known as the refractive index gradient. The slope of the refractive index profile at any point is referred to as distance. The reciprocal of a unit of distance is used to express the refractive index gradient. As we know,the speed of light in the vacuum, $c = 3 \times {10^8}\,m.{s^{ - 1}}$.The universal physical constant $c$, or the speed of light in vacuum, is essential in many fields of physics.

Now, we have to find the speed of light in water- So, we will apply the formula of refractive index in the terms of speed of light:-
$n = \dfrac{c}{v}$
where, $n$ is the refractive index of water, $c$ is the speed of light in the vacuum, and$v$ is the speed of light in water.
$\Rightarrow 1.33 = \dfrac{{3 \times {{10}^8}}}{v} \\\ \Rightarrow v = \dfrac{{3 \times {{10}^8}}}{{1.33}} \\\ \therefore v = 2.25 \times {10^8}\,m.{s^{ - 1}}$
Therefore, the required speed of light in water is $2.25 \times {10^8}\,m.{s^{ - 1}}$.

Hence, the correct option is B.

Note: Water has a refractive index of 1.3 , while glass has a refractive index of 1.5. We know that the refractive index of a medium is inversely proportional to the velocity of light in that medium because of the equation $n = \dfrac{c}{v}$ . As a result, light travels quicker through water.