(a) State and explain the laws of refraction of light with the help of a labelled diagram.(b) What is meant by the refractive index of a substance?(c) Light travels through air at 300 million $ms^{-1}$. On entering water it slows down to 225 million $ms^{-1}$. Calculate the refractive index of water.

(a) Laws of refraction of light:

First Law of refraction: The incident ray, the refracted ray, and the normal at the point of incidence, all lie in the same plane.

Second Law of refraction: The ratio of sine of angles of incidence to the sine of angle of refraction is constant for a given pair of media. This law is also known as Snell’s law of refraction.

 (b) If i is the angle of incidence and r is the angle of refraction, we get:

$\frac {sin\ i}{sin\ r}=constant$

This constant value is called the refractive index of the medium in which light enters through air. The refractive index of a medium can also be expressed in terms of speed of light as follows:

$_1\ n_2=\frac {speed\ of\ light\ in\ medium 1}{speed\ of\ light\ in\ medium\ 2}$

Here, $_1\ n_2$ is the refractive index of medium 2 with respect to medium 1.

(c) Given:

Speed of light in air = 300 million $ms^{-1}$.

Speed of light in water = 225 million $ms^{-1}$.

To find: Refractive index of water.

Solution:

$Refractive\ index\ of\ a\ medium=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ medium}$

Here, 

$Refractive\ index\ of\ water=\frac {Speed\ of\ light\ in\ air}{Speed\ of\ light\ in\ water}$  

$Refractive\ index\ of\ water=\frac {300\ million\ ms^{-1}}{225\ million\ ms^{-1}}$

$Refractive\ index\ of\ water=1.33$

Thus, the refractive index of water is 1.33.

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Updated on: 10-Oct-2022

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