1. F ORMATION OF B EAUTIFUL R AINBOW Done by: Phoe Chuan Bin 28 2O2

2. C ONTENTS 1. Introduction to light dispersion 2. Refraction and reflection of light in water droplet 3. Maximum angle at which light should leave droplet to see the rainbow 4. Rainbow as a 3D cone

3. I NTRODUCTION TO LIGHT DISPERSION What is light dispersion? - Speed of light is slower in various materials than in others -When the light passes into a material at an angle  light beam is bent or refracted  speed of light through a material varies slightly with the wavelength or frequency of the light. Therefore, Each wavelength is refracted at a slightly different angle when passing through a material at an angle. This spreading out of the beam of light is called Light Dispersion E.g. Sunlight passes through a glass prism.

4. Layman terms - Visible light, also known as white light, consists of a collection of component colours. - These colours are often observed as light passes through a triangular prism. Upon passage through the prism, the white light is separated into its component colours - red, orange, yellow, green, blue and violet. The separation of visible light into its different colours is known as Light Dispersion

5. R EFRACTION AND REFLECTION OF LIGHT IN WATER DROPLET The boundary surface between water and air can both Reflect and Refract. o Reflection of light in water droplets - Normal laws of reflection - Angle of incidence equals angle of reflection * All angles are measured from the perpendicular of the surface

6. Refraction of light in water droplets - Angle it bends depend of the 2 media - In our case is water and air - Snell law, Sin A = 1.33 Sin B * A = angle with the perpendicular in air B= angle with the perpendicular in air

7. M AXIMUM ANGLE AT WHICH LIGHT SHOULD LEAVE DROPLET TO SEE THE RAINBOW The angle between the refracted light and the normal to the drop surface is greater than a critical angle, the light reflects off the back of the drop. Since the critical angle for water is 48 degrees relative to the normal. Therefore, if light strikes the back of a raindrop at an angle greater than 48 degrees, it will be reflected back. If the angle is smaller than 48 degrees, the light will simply pass on through.

8. Then, the reflected light is refracted as it exits the drop. Violet light which bends the most, emerges at an angle of 40 degrees relative to the incoming sunlight Red light which bends the least exits the drop at an angle of 42 degrees. Therefore, Maximum angle at which light should leave droplet to see the rainbow = 180- 42 degrees 132 degrees = 132 degrees

9. R AINBOW AS A 3D CONE Refer to: http://www.phy.ntnu.edu.tw/ntnujava/index.php? topic=44 You can see from this website that rainbows are actually a 3D cone where half it is above ground while the other half underground. http://www.phy.ntnu.edu.tw/ntnujava/index.php? topic=44

10. B IBLIOGRAPHY http://www.school-for- champions.com/science/light_dispersion.htm http://orion.math.iastate.edu/lhogben/classes/rain bow.pdf http://www.phy.ntnu.edu.tw/ntnujava/index.php? topic=44 http://www.google.com.sg/imghp?hl=en&tab=wi