Why are rainbows shaped like an arc? How do they just appear in mid-air?We know that we see things because light bounces off an object and into our eyes. However, there is no object in the...

Why are rainbows shaped like an arc? How do they just appear in mid-air?

We know that we see things because light bounces off an object and into our eyes. However, there is no object in the sky where we see the rainbow. How then do we see a rainbow? And, is it possible to calculate the thickness of ONE ray?

Asked on by limjiahui

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The rain bow apprears normally for us  the observers on the earth appearing  in the sky, opposite to sun . But rain bow can happen anywhere a spray of water sprinkling situation exits and a bright light is passing through it (preferably from behind the observer for good vissibility).The happenig of rain bow is on account of the principle of dispersion of light due to refraction and the principle of total reflection of the light through a collection of water droplets ,each acting as a tiny prism. The rain bow is thus an observer's eye specific, and it is not created or formed  on anything like a screan, cloud or hill. In physics the phenomina could resemble a virtual image and not real image like.

The shape of rainbow is an arc or full circle depending on the obervers place.This is so because, the sensation of the rain bow  to the oberving eye is particularly due to only those  droplets of rain acting like of the small prisms on the vision cone of the observers eye. The refraction and total reflection happens at all angle of incidence  but it is of maximum intensity when the incident sun ray on the rain droplet  and refracted and totally reflected ray recieved by the eye, make an angle of 40 to 42 degree(approx). Therefore  the rain droplets that are at  42 degree at our vision cone (the vertex of the vision cone subtending 40 to 42 degree at the observers eye) are resposible for the sensation of circular arc . The upper part of  the circular arc , therefore, appears to have emanated from the sky, whereas the other part appears to have hidden below the horizon.

A person travelling in an aeroplane could sense a full circular shape of rainbow.A person on the top of a hill can also sense  circular rainbow when the sun is behind and the rays are incident on water dropplet below the horizon  due to rain , water fall or mist.

Hope this helps.


krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

It is true that we see things because of light falling on the retina of our eyes. But it not necessary that such light falling on the retina of our eyes should always be reflected off the object. For example, we see sun because of the light directly emitted by it. But we see moon because of light of sun reflected off the surface of moon.

We see rainbow because of the sunlight that come to our eyes passing through tiny drops of water that are present in all clouds. The sunlight consists of a mixture of light of all the seven colours of the rainbow. When light of all these seven colours present in the sunlight is mixed together it forms the white sunlight we normally see. However, due to a phenomenon called refraction, when the sunlight passes through these tiny drops of water, at some specific angles, the lights of different colours bend to different degrees. Because of this we are able to see different colours of lights separately.

The rainbow is shaped like an arc because, the separation of lights of different colours reaching the observer of rainbow occurs only when the light passes those water drops that are situated in atmosphere at a narrow band of angle from a horizontal axis passing through observers eye. All these water drops are situated in an arc shaped formation. The rainbow that we see is because we see different colour of lights of different colours refracted by water drops in different position with respect to our eyes.. There are seven such adjoining strips of water drops, each for one colour of the rainbow.

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