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

Hint: 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 $ ).