Question

If the index of refraction of water is $1.33$, what is the speed of light in water?

Answer 1

Hint: To solve this problem, we have to use the formula of refractive index where we get the relation between refractive index, the speed of light and the speed of light in water. The refractive index is the ratio of speed of light to speed of the light in water. Speed of light is a constant term which is known to us. The SI unit of the refractive index is unit less and speed is meter per second.

Complete step by step answer:
As per the given problem we have to find the speed of light in water where the refractive index is given to us.We know that, refractive index is the ratio of the speed of light to the speed of water.Mathematically can write,
$\mu = \dfrac{c}{v}$
Where, the speed of light is $c = 3 \times {10^8}m{s^{ - 1}}$ which is a constant term.The speed of light in water is $v$ which we have to find.

The refractive index is $\mu = 1.33$.Now putting the given values we will get,
$1.33 = \dfrac{{3 \times {{10}^8}m{s^{ - 1}}}}{v}$
Rearranging the given equation we will get,
$\therefore v = \dfrac{{3 \times {{10}^8}m{s^{ - 1}}}}{{1.33}}$

Hence the speed of the light in water is $v = 2.25 \times {10^8}\,m{s^{ - 1}}$.

Note: Refractive index is a dimensionless number as it is that ratio of two same term speeds of different mediums. Refractive index of medium describes how fast light travels through a medium. Note that higher the reflective index of a medium the slower the light travels in it as it has an inverse relation with the speed of light in medium.