Question

The absolute refractive index of water is $\dfrac{4}{3}$ . What is the critical angle?

Answer 1

To solve this problem we have to know how absolute refractive index and critical angle between two mediums are related to each other. The law which links these two fundamentals is called Snell’s Law. To solve this we simply apply Snell’s law between the two media and we get the answer.

Complete step by step solution:
First let us define Snell’s Law: It is a formula which defines the relationship between the angle of refraction and angle of incidence, when light is travelling through a boundary between two dissimilar media.
Snell’s law states that ratio of the sine of incidence angle and refraction angle is equal to the ratio to
the reciprocal of refractive indices of the given medias, that is: $\dfrac{{\sin {\theta _1}}}{{\sin {\theta _2}}} = \dfrac{{{n_2}}}{{{n_1}}}$.
Now seeing the given problem, we see that we are given one media as water with its refractive index given as $\dfrac{4}{3}$ . Thus, the other media here is air with Refractive index unity.
Now it is said in the problem that we have to calculate critical angles. We know critical angle is the greatest angle at which a ray of light travelling from a denser medium to a rarer medium can strike at the boundary between them so that the light is completely reflected into the denser medium. The angle of refraction is $90^\circ$.
Now applying the above discussed concepts we get:
Critical Angle = ${\sin ^{ - 1}}\left( {\dfrac{{{n_2}}}{{{n_1}}}} \right)$ but here the second media is air
Thus, Critical Angle = ${\sin ^{ - 1}}\left( {\dfrac{1}{{{n_1}}}} \right)$
$\Rightarrow C = {\sin ^{ - 1}}\left( {\dfrac{3}{4}} \right)$
Thus, calculating we get the angle as C = $48.59^\circ$ .

Note: We need to use the Snell’s law and its applications to solve these questions. Keep in mind the relationship and do not get confused. An easy way to remember is that the product of sin angle and refractive index of one media is equal to the product of sin angle and refractive index of the other media. ( $\sin {\theta _1} \times {n_1} = \sin {\theta _2} \times {n_2}$ ).