Laws Of Refraction, Snell’s law: Application, examples, and summary.

In this article, we will study the Laws of refraction. Earlier we have discussed the laws of reflection, Definition, and types of reflection, Particle nature of light, reflection at the plane mirror, and other topics.

What are the laws of refraction?

Refraction at any surface is always governed by two laws. these laws are also known as Snell‘s law of refraction due to the scientist who discovered these laws.

First law of refraction:

Statement: The first law of refraction states that The incident ray refracted ray, and the normal to the interface of media at the point of incidence, all lie in the same plane. this can be further illustrated by the figure given below

Explanation:

Second law of refraction:

Statement: The second law of refraction states that for a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is always a constant. This law is also known as Snell’s law of refraction. This law holds great significance in ray optics. let us understand this law with an example.

Explanation:

Example: consider two mediums medium 1 and medium 2. suppose a ray from medium 1 falls on the surface of medium 2. The ray will get refracted to the medium 2. here the angle of incidence is denoted by i and the angle of refraction is denoted by r. so according to the second law of refraction

$\mathbf{\frac{Sin(i)}{Sin(r)}= n_{21}}$

This law is also known as snell’s law of refraction.

This constant is called the refractive index of medium 2 with respect to medium 1. denoted by $n_{21}$

Application of Laws of refraction:

1. Microscope and Telescopes: Many optical devices work according to the laws of refraction. A deep understanding of the laws of refraction helps us to build and manipulate these devices according to our needs.
2. The formation of mirages, the twinkling of stars, total internal reflection, and many other phenomena can be explained by the laws of refraction.
3. Formation of VIBGYOR when light passes through the prism.

Read Also

Simple microscope Class 12, Definition, Magnification, working, Parts And Uses

Examples of the laws of refraction:

Question 1:

A ray of light travels from air to an optical fiber whose refractive index is 1.44.  Find

(a)  does light bends towards the normal ray or away from the normal ray? 

(b)  If the angle of incidence is 22^o, what is the angle of refraction? 

(c) Draw a labeled diagram for the given situation.

Solution:

(a) The optical density of air is lower than the optical fiber, so the light will bend towards the normal ray.

(b) let us denote the air as medium 1, and optical fiber as medium 2. Also, according to question n$_{1}$=1.00 and $n_{2}$=1.44. According to Snell’s law $$\mathbf{\frac{Sin(i)}{Sin(r)}= n_{21}}$$

so, (1.00) sin 22^o = 1.44 sin θ₂.
sin θ₂ = (1.00/1.44) sin 22^o = 0.260
θ₂ = sin^-1 (0.260) = 15^o.

(c)

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Sample Problem – 2

A ray of light traveling through an optical fiber of refractive index n=1.44 reaches the end of the fiber and goes into the air.

  (a) If the angle of incidence is 30^o, what is the angle of refraction? 

(b)  what if the angle of incidence were 50^o?

Solution:

(a) sin θ₂ = (1.44/1.00) sin 30^o = 1.44 (0.500) = 0.720
θ₂ = sin^-1 (0.720) = 46^o.

(b) If we replace the angle of incidence with 50^o it gives
sin θ₂ = (1.44/1.00) sin 50^o = 1.44 (0.766) = 1.103. This equality cannot be met, so light cannot exit the fiber under these conditions.

The situation in part (b) is an example of total internal reflection.

Summary

There are basically two laws of refraction, the first one tells that this phenomenon happens in the same plane, and the second law gives the relation between the angle of incidence, angle of refraction, and the refractive indices of mediums. These laws have a wide range of applications in so many fields.