When we look at a rainbow, we are reminded of hope. A hope that even at the end of a rainy day, a beautiful and colourful light symbolising happiness emerges. It is a truly wonderful sight to witness. It is also a source of amusement to children as they hear tales of a pot of gold at the end of the rainbow. But at the end it is just another marvel of physics. It can be explained through optics. “Optics” is a branch of physics that studies the properties of light. There are three different hypotheses on the mode of propagation of light. The three modes are wave propagation, through straight lines or rays and in the form of energy particles called photons. These modes of propagation were proposed to explain the different theories and properties of light.
“Visible light” is a part of the electromagnetic spectrum with a wavelength falling between UV rays and Infrared rays. Visible light itself is further sub divided into different colours at different wavelengths which ranges from red with the shortest wavelength to violet with longest wavelength. These are the rainbow colours in order which we notice while looking at it. A rainbow is a multi coloured arc formed with the order of colours being R (Red), O (Orange), Y (Yellow), G (Green), B (Blue), I (Indigo) and V (Violet) from top to bottom. There are three properties of light in play when we observe a rainbow. In its correct order of occurrence, they are: Refraction, dispersion of light and Total Internal Reflection. To explain the linked mechanism of all these properties, light is considered to travel as a ray (straight line propagation of light). Let us study the formation of a rainbow part by part while understanding each property.
Formation of Rainbow
Formation of Rainbow Step 1 – Refraction:
What is Refraction? – When light passes from one medium to another possessing different density the light ray bends at an angle. When the light passes from a rarer medium to a denser medium the light bends towards the normal to the surface of the second medium and away from normal while passing from a denser medium to a rarer medium. We can observe this when we see through a swimming pool. The floor appears to be higher than it actually is. The light rays coming from the floor to the eye go through a change of medium from water (denser) to air (rarer) and hence appears to be higher.
Refraction of Sunlight – So in the case of a rainbow formation, the light comes from the sun which passes through suspended water droplets. Here the sunlight is passing from a rarer medium (air) to a denser medium (water).
Formation of Rainbow Step 2 – Dispersion:
What is Dispersion? – White light consists of lights of seven different monochrome rays each of which has its own wavelength. So, when white light undergoes refraction, each colour bends at a different angle causing the splitting of the light depending on its wavelength. The difference between the angles of deviation is very small. So when theses split lines undergo refraction again, the angle difference increases and the colours are more noticeable. Therefore during dispersion white light is split up into its constituent colours.
Dispersion of Refracted Sunlight:
After the refraction has occurred from the rain drop, the white light from the sun undergoes dispersion and splits into its constituent colours. The red light undergoes the leastdeviation from the incident light which causes its formation on the top while violet undergoes the highest deviation to get a bottom spot.
Formation of Rainbow Step 3 – Total Internal Reflection:
What is Total Internal Reflection? – Total internal reflection occurs when a light ray passes from a denser medium to a rarer medium. When the incident angle of light on the boundary of the denser medium is more than a particular angle called the “Critical Angle” of that medium, then the light ray gets reflected back rather than being refracted. The optic fibres that we use in our homes for telephone lines, cable lines and broadband lines use this principle to transmit signals through long distances and with minimal signal loss. We can even observe this property by taking a plane piece of glass. First we must look at it normal to its surface and gradually increase the angle. After a particular angle, we notice that the glass starts to act like a mirror, no longer enabling us to see beyond it.
Total Internal Reflection of Light Rays Inside Water Droplets
The dispersed beams of white light get refracted through the first surface of the water droplet. When they are incident on the second surface (outer surface) with an angle more than the critical angle, the rays undergo total internal reflection and bounce back to the first surface and again undergo refraction and finally reach the eyes of the observer.
Putting the pieces together
On the other hand, Rainbows are also formed at the end of a waterfall at the place where the fine mist is present. To witness a rainbow, a bright sunlight, suspended water particles and the proper angle of viewing are essential. We can observe a rainbow when our back is faced towards the sun, there are suspended water particles in the air in front of us and that the angle of the water particles and our eyes is between 40 and 44 degrees.
Rainbows are actually formed in circular shapes. We generally see an arc shaped rainbow because of the presence of the ground since the suspended water particles are no longer present. Rainbows which are witnessed from aircrafts are observed to be in full circles since the angle is such that the suspended water particles are below us. But why do rainbows take a circular shape rather than the entire sky getting coloured up?
The angle difference between the ends of the rainbow (Violet and Red) is approximately two degrees i.e., the red light is deviated to an angle of 42 degrees from the incident angle of white light and violet light is deviated by an angle of 40 degrees. This deviation occurs at the suspended water particles that are at the correct angle ofviewing. Since every point is equidistant from the centre of a circle, the locus of the rainbow formed takes shape of a circle. All the suspended water particles that cause this angle of deviation are present on this circular locus with the observer being at the centre.