Introduction

Light is considered by many scientists to have dual nature, both particle nature and wave nature. First, Particle nature is one in which we consider a stream of packets of energy called photons. Second, Wave nature is considering light as electromagnetic radiation whereas part of it is perceived by humans. Visible spectrum defined by humans lies in a range of 400 to 700 nm wavelengths.

Behavior of light is different when it passes from one medium to another, the speed varies in different mediums of light. This variance in speed leads to bending of light at point of incidence when it crosses from one medium to another, the whole phenomenon is known as refraction and the angle at which the rays come out is known as angle of refraction.

Some practical example of refraction which we see in day to day life but goes unnoticed are, first specs, almost each one have used it or seen once in life and it is based on concept of refraction, we see sun few minutes after sunset is due to refraction, the objects in water appears larger or different and like these many more can be given.

Concept

Medium implies like air is a type of medium, similarly water is an example of another medium. They have distinct properties which make them distinct from one another. Some distinct properties like density, transparency etc. which makes one medium from another.

For example, water is denser than air, honey is denser than water. The behavior of light in these two mediums will be different due to their distinct properties. But this difference is more apparent when light travels from one medium to another.

Consider an example, when one puts their hand in a bucket of water, your fingers look bigger. But does the size of the finger increase? Definitely not, but they appear to be bigger; this is an example of refraction.

When light travels from one medium to another the light gets deviated from its path at the point where it crosses the medium, this phenomenon is known as Refraction and the light is called as refracted. Refer to the figure above.

Cause of Refraction

The change occurs due to change in speed in light, rather we can say the speed of light changes when it travels from one medium to another. For example, the speed of light is maximum in vacuum, and speed will be less in air, and even less in water.

The Phenomena

From figure 1, the light goes from air to water i.e., from a less dense medium to denser medium. This light can be seen deviated from its actual path of travel; it moves closer to the line of normal. The line of normal is drawn at the intersection of two mediums and refraction is measured in terms of an angle with respect to normal.

The blue line in figure 1 is the incident line or incident ray, and of incident line with the normal is known as angle of incidence, represented as ${\theta }_i$. The red in figure 1 shows refracted light or the deviated light. The angle of refracted ray with the normal is known as angle of refraction, represented as ${\theta }_r$.

The refraction is directly related to change in speed of light when the medium changes. The larger is the change in speed, the larger will be the refraction observed.

As we have density as property of any medium, for electromagnetic waves, the speed of light in any medium depends on its optical density. It is not the same as density, which is defined as ratio of mass and volume. But it could be said similar to it. The speed of light will be lesser in the medium whose optical density is larger and vice versa. The optical density of any material is indicated by the index of refraction value. It is represented as the ratio of speed of light in vacuum to that of speed of light in the given medium, i.e. how much slower the light will be compared to its speed in the vacuum. The index of refraction value of vacuum is 1.

Snell’s law or law of refraction gives the relation between angle of incidence, angle of refraction and indices of refraction values of mediums. It is represented as follows$n_i*sinsin {\theta }_i= n_r*sinsin {\theta }_r$,

Where,

$n_i=index of refraction for incident medium$ $n_r=index of refraction of refractive medium$ ${\theta }_i=angle of incidence$ ${\theta }_r=angle of refraction$

Problem (based on Snell’s Law)

Question: An engineering student uses optical fiber of experimental purpose, such that light traveling through it exits in air from one end. For the given angle of incidence at the end of fiber of 20 degree, calculate angle of refraction. Index of refraction for optical fiber is 1.42 and the index of refraction for air is 1.

Solution: Applying Snell’s law,

$n_i*sin {\theta }_i= n_r*sin{\theta }_r$ ,

$1.42*sin 20= 1*sin {\theta }_r$

Hence, $sin{\theta }_r =0.485$

${\theta }_r=si{n}^{-1}\left(0.485\right)$

${\theta }_r={29.01}^o$

Application

When light travels from optically denser to less optically denser medium, the light gets refracted away from normal. There will be an angle at which the light will get reflected back in the same medium, this angle is called a critical angle, beyond this angle if incidence angle is greater, the light will not go in another medium, rather it will be totally reflected in the same medium itself. The angle of refraction becomes 90^o at critical angle.

$({\theta }_c=\frac{n_1}{n_2} )$

Where,

$n_1=index of refraction of optically more dense medium$ $n_2=index of refraction of optically less dense medium$

Optical fiber is one of the best applications of total internal refraction. Here the data travelled on the concept of TIR. It is used in modern day communication systems and finds great application in the medical field in micro surgeries. Major benefit of this is, there is no loss of data and energy during transmission, hence the intensity of signals remains constant throughout the communication.

A very common example of TIR is the shine we see in the diamond, these diamonds are cut in such an angle that light entering the diamonds goes though TIR.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for      

• B.Sc. Mathematics
• M.Sc. Mathematics