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Formation of Rainbow

Formation of Rainbow. Introduction. We usually only see rainbow after a shower of rain, and it also occurs in waterfalls and ocean waves . This is because water droplets is essential in the formation of rainbow.

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Formation of Rainbow

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  1. Formation of Rainbow

  2. Introduction • We usually only see rainbow after a shower of rain, and it also occurs in waterfalls and ocean waves. This is because water droplets is essential in the formation of rainbow. • Basically, rainbow is formed when white light dispersed, reflected and refracted by water droplets.

  3. The Steps Involved in the Process 1. Sunlight strikes water droplet 2.Reflection of light at the surface of water droplets3.Refraction of light – light entering the water droplet4.  Light dispersion5.Total internal reflection occur at the water-to-air interface6.Refraction of light- light leaving the water droplet7.Further light dispersion

  4. Step1 : Sunlight strikes water droplets Before we start, let’s think about when we usually sees rainbow: • After a shower of rain • Dawn or late afternoon

  5. Step1 : Sunlight strikes water droplets • But why can’t we sees rainbow at night, or when it doesn’t rain? • It is because sunlight and water droplets are essential in the formation of rainbow.

  6. Step1 : Sunlight strikes water droplets • But even if it rain, we still seldom sees rainbow during early morning, middle afternoon or late evening. • It is because the sunlight must strike the water droplets at a certain angle before the formation of rainbow is possible. • It is best if the sun is fairly low in the sky such as dawn and late afternoon.

  7. Step2: Reflection of light at the surface of water droplets • 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. 

  8. Step2: Reflection of light at the surface of water droplets • Similarly, 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 sun light hits a water droplet, some of the light is being reflected. This light will obey the Law of Reflection. 

  9. Step2: Reflection of light at the surface of water droplets • Recap - Law of reflection • The angle of incident (i) must be equal to the angle of reflection (r).

  10. Step3 - Refraction of light – light entering the water droplet • Refraction occur when a light wave passes from one medium to another. The light slows down when travel to a denser medium. Thus the light will bent towards to the normal so that the angle of incident (i) is greater than the angle of reflection (r)

  11. Step3 - Refraction of light – light entering the water droplet • For example, in the picture below, the light is refracted in the glass block because the glass block is denser than the air, thus the light slows down and bend toward the normal when passing through the glass block

  12. Step3 - Refraction of light – light entering the water droplet • Similarly, water can also refract light. After reflection of light occur at the surface of the water droplets, the rest of the light will enter the water droplet and being refracted.

  13. Step4: light dispersion • A beam of white light (e.g. sunlight), is made up of wavelengths of different colours of light. • Different wavelengths travel at different speeds. When they encounter a change to medium that is more dense or less dense, the speeds are affected by different amounts. Hence, the colours separate. • This phenomenon is know as Dispersion. 

  14. Step4: light dispersion • For example, when a beam of white light passed through a prism, the beam of light is dispersed and the colours are separated.

  15. Step4: light dispersion • Such process could also seen when light passed through water droplets. • The picture below shows white light incident on a drop of water on a CD resulting in dispersion

  16. Step4: light dispersion • Basically, the colours dispersed are Red, Orange, Yellow, Green, Blue, Indigo and Violet in that order respectively. • Each colour has different wavelength, as shown below.

  17. Step4: light dispersion • Violet light has a higher frequency and energy than red light. Hence violet light travels slightly faster than red light. The result of this difference is that when white light is refracted, the violet component is bent most and the red component is bent least.

  18. Step4: light dispersion

  19. Step4: light dispersion • Therefore, this resulted a violet light to be located in the inner section of the rainbow and red light to be located in the outer section of the rainbow. This same principle explains the reasons for the order in which the different colours of light appears in a rainbow.

  20. Step5: Total internal reflection occur at the water-to-air interface   • At the water-to-air interface of the water droplets, total internal reflection will occur if the angle of incident is greater than the critical angle. • Wait, what is critical angle?

  21. Step5.1: Critical Angle • The critical angle is the angle of incident above which total internal reflection occurs. Which its angle of reflection must be 90 • If the angle of incident is greater than the critical angle, total internal reflection will occur. • If the angle of incident is smaller than the critical angle, the light will be transmitted.

  22. Step5.1: Critical Angle • Critical angle can be calculated using snell’s law, where: • sin I / sin r = n* • Sin I = (sin) angle of incident • Sin r = (sin) angle of reflection • N* = Relative refractive index

  23. Step5.1: Critical Angle Given that the relative refractive index of water-air interface is 0.752, thus we can adapt snell’s law to calculate critical angle of this water-air interface. n* =   0.752ic=  Critical angle  r   =  Angle of refraction Note sin 90 = 1 Thus, we sees that the critical angle of water-air interface is 48.75

  24. Step5: Total internal reflection occur at the water-to-air interface  • So, after know that the critical angle of Water-air interface is 48.75 , we know that total internal reflection will occur if the angle of incident greater than the 48.75 . • Thus link this back, we now sees that why the sunlight must strike the water droplets at certain angle to form rainbow, it is to enable total internal reflection to occur.

  25. Step5: Total internal reflection occur at the water-to-air interface  • After fulfilling the critical angle (angle of incident > critical angle), the total internal reflection is just normal reflection of light which follows the laws of reflection (angle of incident = angle of reflection) The picture show the total internal reflection of the red ray

  26. Step6: Refraction of light - light leaving the water droplet • In the other way round, when light travel from a medium to another less dense medium, the light will travel at a greater speed. Thus the light will bent away from the normal so that the angle of incident (i) is smaller than the angle of reflection (r)

  27. Step6: Refraction of light - light leaving the water droplet • Thus, when light travels back out of the raindrop, refraction occurs. The diagram below shows the angles for the violet ray.

  28. Step7: Further light dispersion • Thus, after the sunlight leaves the water droplets, it is being refracted again. Hence it will increased the separation of the component colours of white light again. (dispersion) • The rainbow is finally formed when sunlight dispersed, reflected and refracted through thousands of water droplets in the atmosphere.

  29. Where/How should we observe rainbow? • No two person will see exactly the same rainbow • A "rainbow" is not a physical object, and cannot be physically approached.

  30. A rainbow is always directly opposite the sun from the observer. That is, the rainbow appears in front of the observer, whose back is to the sun.

  31. We see a rainbow at 42 degree angle, it is measured from each observers eye thus therefore, no two persons will see exactly the same rainbow.

  32. Rainbow as 3D cone • Rainbow go through similar processes (dispersion, reflection and refraction) inside a 3D cone that filled with water. • Watch the following video: • http://www.youtube.com/watch?v=vvZEbkAzaCc

  33. Sources • http://www.myuniversalfacts.com/2006/04/how-rainbows-are-formed-what-causes.html • http://rebeccapaton.net/rainbows/formatn.htm • http://answers.yahoo.com/question/index?qid=20080224093631AANR2kk • http://www.soulaura.com/2010/07/3d-volumetric-laser-scanner-rainbow-cone-pentagon/ • http://en.wikipedia.org/wiki/Rainbow

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