Question

Refractive index of water and glass are $\dfrac{4}{3}$ and $\dfrac{3}{2}$ respectively. A ray of light travelling in water is incident on the water-glass interface at $30^\circ$ . Calculate the sine of the angle of refraction.
A. $0.460$
B. $0.585$
C. $0.444$
D. $0.623$

Answer 1

You can start by giving a brief definition of Snell’s law and also write the equation of Snell’s law $\dfrac{{{\mu _2}}}{{{\mu _1}}} = \dfrac{{\sin i}}{{\sin r}}$ . Then put all the corresponding values in the equation and calculate the value of $\sin r$ .

Complete answer:
Snell’s law defines a formula that establishes a relation between the angle of incidence and the angle of refraction, for a ray of light travelling from one medium to the other. Snell’s law is based on the fact that light travels with different speeds in different mediums and shows a bending effect when it travels from one medium to the other.
In this problem we are given a ray of light travelling from water to glass, the angle at which the ray of light strikes the water-glass interface is $30^\circ$. We are also given that the refractive index of water and glass are $\dfrac{4}{3}$ and $\dfrac{3}{2}$ respectively.

According to Snell’s law
$\dfrac{{{\mu _2}}}{{{\mu _1}}} = \dfrac{{\sin i}}{{\sin r}}$
Here, ${\mu _2} =$ The refractive index of the medium that ray of light travels to.
${\mu _1} =$ The refractive index of the medium that ray of light travels from
$i =$ The angle of incidence
$r =$ The angle of incidence

So, given ${\mu _2} = \dfrac{3}{2} =$ Refractive index of glass
${\mu _1} = \dfrac{3}{2} =$ Refractive index of water
And $i = 30$
So, for this particular problem, the equation of Snell’s law becomes
$\dfrac{{\dfrac{3}{2}}}{{\dfrac{4}{3}}} = \dfrac{{\sin 30^\circ }}{{\sin r}}$
$\Rightarrow \dfrac{{3 \times 3}}{{2 \times 4}} = \dfrac{{\dfrac{1}{2}}}{{\sin r}}$
$\Rightarrow \sin r = \dfrac{4}{9}$
$\Rightarrow \sin r = 0.444$

So, when the ray of light is incident on the water-glass interface at $30^\circ$, the angle that the refracted ray makes with the normal is $0.444$.

So, the correct answer is “Option C”.

Note:
In the given problem we are required to calculate the value of $\sin r$ . But you may also face problems where you have to calculate the value of $r$ . Most of the time the values are very simple and common trigonometric function like $30^\circ$ , $60^\circ$ , etc. but sometimes like in this problem you have to use the trigonometric table to find the answer (in this case $r = 26.8^\circ$ ).