The rainbow happens due to the refraction of sunlight in the water droplets that are suspended in the atmosphere.
Well, in Physics we define refraction as the phenomenon that occurs when light passes from one propagation medium to another. In this change of medium, the light undergoes a deflection, that is, it undergoes a change in its propagation speed. It is also worth remembering that the first law of refraction says that both the incident ray, the refracted ray and the line normal to the surface that separates the two media belong to the same plane.
The second law of refraction is also known as the Snell-Descartes Law. This law states that the product of the index of refraction of the medium by the sine of the angle that the ray makes with the normal line has a constant value. Therefore, mathematically we can write the second law as follows:
n 1 .seni= n 2 .sinr
In refraction, when a ray of light changes medium, that is, when the ray passes from a medium of propagation to another medium whose refractive index has a lower value than the first, the ray of light is refracted. In this refraction, the light ray then tends to depart from the normal line. In this case, we can observe that, depending on the angle of incidence, refraction will no longer occur, therefore, this angle is called the limiting angle and this angle depends on each pair of refracting surfaces.
Below we will see how we can determine the value of the limiting angle.
n 1 .sinL= n 2 .sin 90º
As the value of sin 90º = 1, we can make this substitution in the equation above, in order to determine the value of L. Therefore, we have:
n 1 .sinL= n 2 .1
We can see from the equation above that the sine of the limiting angle depends on the two refractive indices of the incident and refracted media. By the equation, sin L is nothing more than the quotient of the refractive index of the less refractive medium by the refractive index of the most refractive medium. So, we write:
It is worth remembering that when the angle of incidence is greater than the limiting angle, refraction ( i > L ) will not occur, so all rays that fall on the surface will be reflected. The phenomenon in which rays are reflected will be called total internal reflection.