Thursday, February 12, 2015

How Do Rainbow Form

Rainbows appear in seven colors because water droplets break sunlight into the seven colors of the spectrum. You get the same result when sunlight passes through a prism. The water droplets in the atmosphere act as prisms, though the traces of light are very complex.
When light meets a water droplet, it is refracted at the boundary of air and water, and enters the droplet, where the light is dispersed into the seven colors. The rainbow effect occurs because the light is then reflected inside the droplet and finally refracted out again into the air.

Rainbows: Refraction of the Seven Colors of the Spectrum
A rainbow has seven colors because water droplets in the atmosphere break sunlight into seven colors. A prism similarly divides light into seven colors. When light leaves one medium and enters another, the light changes its propagation direction and bends. This is called refraction. However, because of differences of refractive index, this refraction angle varies for each color or according to the wavelength of the light. This change of the angle of refraction, or refractive index, in accordance with the wavelength of light is called dispersion. In conventional media, the shorter the wavelength (or the bluer the light), the larger the refractive index.

Refraction Depends on Light's Color and the Medium
The angle of refraction depends on the speed at which light travels through a medium. People have noticed the phenomenon of refraction throughout history. But the first to discover the law of refraction was Willebrord Snell (1580-1626), a Dutch mathematician. The refractive index of water to the orange sodium-vapor light emitted by streetlamps on highways is 1.33. The refractive index of water to violet, which has a short wavelength, is nearly 1.34. To red light, which has a long wavelength, the refractive index of water is almost 1.32.

Water Droplets Reflect Refracted Light
Sunlight hitting a water droplet (sphere) in the atmosphere will be refracted on the surface of the droplet, and enters the droplet. When the refraction process occurs, the light breaks up into seven colors inside the water droplet, and is next reflected at the other surface of the droplet after traveling inside it. Note that in reflection the angle of reflection is the same as the angle of incidence, which means that reflected light travels in a predetermined path while maintaining the difference of angle of refraction. The light is refracted again when it exits the droplet, further emphasizing the dispersion. The primary reflection of a main rainbow and the secondary reflection from a slightly darker auxiliary rainbow disperse the light into the seven colors our eyes see.

The Visible Angles of Rainbows Are Predetermined

    You can see rainbows when the sun is located right behind you. The main rainbow becomes visible at an angle of around 40" from the horizon. You can see the auxiliary rainbow at about 53". The orders of the colors reflected from the water droplets in the main rainbow and in the auxiliary rainbow are reversed, as shown in the illustration.

    The Process of Rainbow - How Rainbows Form

    rainbow process

    Basic diagram showing formation of rainbow. 

    Angles not to scale.  
    The formation of a rainbow involves a series of physical phenomena - reflection, refraction, dispersion and total internal reflection. 
    The occurence of each of these is due to the interaction of light with air and water and the boundaries between them. 

      The Steps Involed in the Process

      Figure 2:  Ray digram - light through raindrop

        1. Light from sun strikes raindrop.

        White light from the Sun has to hit the raindrops at a certain angle before a rainbow is possible. It is best if the sun is fairly low in the sky such as dawn and late afternoon. The angle is important as it effect the direct the light travels after it hits the raindrops and that determines whether or not we will see a rainbow.

        2. Some of the light is reflected.

        It is possible to see through a glass window but, at the same time, see your own reflection. This is because the window both transmits and reflects light. Water can do this too - that is why you can see a reflection in a pool of clean water and also see the bottom.When light from the sun hits a water droplet, some of the light is reflected. This light will obey the Law of Reflection.

        3. The rest of the light is refracted.

        The light that is not refracted crosses the air-water interface (boundary layer). When this happens it slows down because the water is more dense than the air. The reduction of speed cause the path of the light to bend - this is called refraction. In this case the path of the light rays bends toward the normal line.

        4. White light splits into component colours.

        White light is made up of a spectrum of colours, each with its own wavelength. Different wavelengths travel at different speeds and when they encounter a change to medium that is more dense or less dense, the speeds are efected by different amounts. Hence, the colours separate. This phenomenon is know as Dispersion.

        5. Light is reflected at rear of raindrop (TIR).

        At the rear of the raindrop, the light hits the water-to-air interface. If the angle of incidence is greater than the critical angle, Total Internal Reflection will occur. A rainbow will only be seen if this happens, otherwise the light will continue out the other side of the raindrop and continue to move away from the would-be viewer.

        6. Light is refracted again as it leaves raindrop.

        Just as the light changed speed as it entered the raindrop, its speed changes again as it leaves. Here, the light is moving from a more dense medium (water) to a less dense medium (air). As it does so, it speeds up and its path bends. In this case the path of the light rays bends away from  the normal line. This is another example of refraction.

        7. Colours are further dispersed.

        As the rays are refracted once again, the various wavelengths are effected to different extents. The overall result of this is increased separation of the component colours of white light. This is Dispersion.