Total Internal Reflection

Rainbows are beautiful creations of nature

The fundamental process at work in a rainbow is refraction -- the "bending" of light

To understand how rainbows are created, we first need to understand the fundamentals of refraction

In vacuum, light has a velocity of $3\times 10^{8}m/s$ denoted by the symbol c

However, when light passes through a medium, the velocity becomes lesser than $3\times 10^{8}m/s$

For different mediums the velocity of light is different

So as light passes from one medium to the other due to change in speed bending of the path of the light occurs

The phenomenon in which the bending of the path of light occurs due to change in the speed of light is known as refraction

Till now we understood how and why refraction occurs

Let us now understand two different cases

The degree to which a refractive medium retards transmitted rays of light is known as the optical density of the substance

As the optical density of a substance increases, and the speed of light in that material decreases

A medium can be of two types on the basis of optical density

It can be optically denser and optically rarer

When light travels from a rarer to a denser medium the path of the light bends towards the normal

When light travels from a denser to a rarer medium the path of the light bends away from the normal

Now that we understand refraction let us understand total internal reflection

We know that when light travels from one medium to a different medium, a bending of path occurs

When light passes from one medium to another, the angle of incidence and the angle of refraction are related by $\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$

$\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$ is known as Snell's law or the law of refraction

In $\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$ i is the angle of incidence and r is the angle of refraction

The angle of incidence is the angle in which light falls on the surface and the angle of refraction is the angle in which it is refracted

${\mu }_1$and ${\mu }_2$ are the refractive indices of the two mediums

The refractive index $\mu$ is defined as $\frac{c}{v}$, where c is the velocity of light in vacuum and v the velocity in a medium

If ${\mu }_1$is the refractive index of the denser medium and ${\mu }_2$ is the refractive index of the rarer medium then ${\mu }_1>{\mu }_2$

When light travels from a denser to a rarer medium the angle of refraction is usually greater than the angle of incidence

That the angle of incidence will be greater can be interpreted from the equation$\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$ as ${\mu }_1>\mu 2$

Now let us consider an angle of incidence such that the angle of refraction is $90°$

The light ray grazes the boundary between the two mediums when the angle of refraction is $90°$

If the incidence angle is such that the angle of refraction becomes greater than $90°$ the light ray is refracted back to the first medium

The phenomenon in which the light ray is refracted back to the first medium is known as total internal reflection

The incidence angle for which the light ray grazes the boundary between the two surfaces is known as the critical angle $({\theta }_c)$

Hence total internal reflection occurs when the incidence angle is greater than the critical angle $({\theta }_c)$

Revision

The angle of incidence(i) and the angle of refraction(r) is related by $\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$ known as Snell's law

The refractive index $\mu$ is defined as $\frac{c}{v}$, where c is the velocity of light in vacuum and v the velocity in a medium

${\theta }_c$ is the critical angle of incidence such that the light ray grazes the boundary between the two mediums

Total internal reflection occurs when the angle of incidence is greater than the critical angle and when the angle of refraction is greater than $90°$

In total internal reflection, the light ray is refracted back to the previous medium

The End