Question

A ray of light travels from a medium of refractive index ${n_1}$ to a medium of refractive index ${n_2}$ . If the angle of incidence is $i$ and angle of refraction sin $r$ , then $\dfrac{{\sin i}}{{\sin r}}$ is equal to ________.
A) ${n_1}$
B) ${n_2}$
C) $\dfrac{{{n_2}}}{{{n_1}}}$
D) $\dfrac{{{n_1}}}{{{n_2}}}$

Answer 1

Hint: You can solve this very easily if you try to recall what Snell's law is. Snell’s law relates the angle of incidence and angle of refraction with the refractive indices of the respective medium. This is exactly what’s being asked in the question above.


Complete step by step answer:
We will be trying to solve the question exactly as we told in the hint section of the solution to the question. But for to do that, we first need to talk about Snell’s law.
Snell’s law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
Mathematically, it can be written as:
${n_1}\sin i = {n_2}\sin r$
Where, ${n_1}$ is the refractive index of the medium from which the light is coming.
$i$ is the angle of incidence from the normal to the common surface.
${n_2}$ is the refractive index of the medium into which the light is going.
$r$ is the angle of refraction from the normal to the common surface.
The question has already given us all the information that we need to solve the question, let’s review the information given.
Refractive index of the medium from which the light is coming $ = {n_1}$
Refractive index of the medium into which the light is going $ = {n_2}$
Angle of incidence from the normal to the common surface $ = i$
Angle of refraction from the normal to the common surface $ = r$
Now, directly using the Snell’s law, we write:
${n_1}\sin i = {n_2}\sin r$
After transposing, we get:
$\dfrac{{\sin i}}{{\sin r}} = \dfrac{{{n_2}}}{{{n_1}}}$
This matches with the option (C) of the question. Hence, option (C) is the correct option.

Note: Basically the light deviates due the change of medium is that light has different speed in different mediums and hence covers different distances in different mediums at the same time. This is a pretty basic question. All you need to have to solve such questions is to have a good grasp on the basic concepts of the topics which are frequently asked in question papers. Such questions can gain you easy and fast marks in any paper.