Colours

The explanation of the rainbows colours was first shown by Isaac Newton around 1667. He had already shown that light was a mixture of colours which could be shown by the use of a prism. In the same way he argued that water droplets in the air dispersed the various colours in various directions, so that the colours of the spectrum were seen.

rainbow 1
The curved appearance of the rainbow was first correctly explained about 1611.

It was attributed to the refraction [bending] of light at a water drop followed by the reflection inside the water drop, the light ray finally emerging into the air. A bit like a prism.
rainbow 2

 

Suns Rays
Primary and Secondary Bow 


Secondary Bow   
Sometimes a secondary bow is seen higher in the sky and is formed by rays undergoing two refractions and two reflections at the "droplet".

 

 

Primary Bow 
The primary bow is the rainbow usually seen which is obtained by two refractions and one reflection as the rain drops fall down from the sky.

 

Deviation of Light by a Sphere

ray of light

Suppose a ray of light, ( shown as a 0 ) in air is incident on a sphere of glass or a drop of water. The light is refracted [bends] at 0, then reflected inside B and finally emerges into the air along the points C and D.

If  i and r are the angles of incidence and refraction at 0 ,the deviation of light at 0 and C is ( i - r ) each  time it is ( 1800 - 2r ) at B

 


The total deviation $ in a clockwork direction can be shown by the following equation.
$ = 2 ( i - r ) + 1800 - 2r = 1800 + 2i - 4r
total deviation

It can be seen that the deviation at each reflection is (i-r) this shows that a ray undergoes two reflections inside the sphere and two refractions as shown below. the total deviation in a clockwise direction is equal to
Deviation of Light by a Sphere

2( i - r ) +2 ( 1800 + 2r )=3600 + 2i -6r.
after n reflections the total deviation
= 2( i - r ) +n ( 1800 - 2r )

Deviation of Ligh

 

Types of reflection

Specular Reflection
Specular Reflection

from a smooth or polished surface.
The angle of incidence is equal to the angle of reflection
Diffuse Reflection
Diffuse Reflection

from a uniformly matt surface.
The brightness of the reflection does not change much with point of view.
Spread Reflection
Spread Reflection

from a semi-gloss finish.
e.g. egg-shell finish.
Diffuse and Specular Reflection
Diffuse and Specular Mixed

Rays from porcelain or synthetic enamel surfaces