Question

why does a rainbow appears in a semicircled shape

Answer 1

formation of a rainbow is shown in the diagram.

It is formed by Sun rays falling on small spherical rain drops suspended in air at a height from ground. These rays get refracted, reflected and refracted to form the Primary rainbow with Violet at the bottom and red at the top.

The violet rays make an angle of about 40 deg with the horizontal and the the red rays make an angle of 42 at our eyes. So red color making higher angle at our eye appears above the violet color in the rain bow.

If we take a cone of angle 42 deg., (or a funnel - we are familiar with it at home) and place our eye at its vertex. Then we will be able to view the rainbow around its circular edge or circumference.   

Its semicircular shape is a result of the geometry and the rules of total internal reflection and refraction thru water.

Answer 2

rain bow is formed when there is sunlight after the rain. each every drop of water act like smallprismsinthe atmosphere.when sunlight is passed through it , it undergoes  refraction and multiple reflection and light get dispersed.but it seems as one drop gives one coloursince they are of different wavelength.all the colours are formed between 40.8deg and 42.8deg red from allthe droplets make an angle of 40.8 deg with the line of vision and violet makes an angle of 42.8 deg .Allother colours are in between .so rainbow is formed in the form of an arc.higher the wavelength lower the deviation so red is the outermost colour of the rainbow