Essay on Effect of a Water Droplet on a Rainbow

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The Formation of a Rainbow

Sir Isaac Newton found that white light is composed of all wavelengths of visible light. White light is a mixture of all the colors of the spectrum, which are: Red, Orange, Yellow, Green, Blue, Indigo, and Violet. If we break up white light we can see the various components. A glass prism can be used to split white light into various wavelengths. This split occurs because each color in the white light has a different index of refraction. Thus, the different colors will respond differently to the glass. For example, blue light will refract more than the wavelengths corresponding to yellow, and yellow light will refract more than the wavelengths corresponding to red. This effect is called dispersion.

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And like prisms, the white light is also refracted and dispersed in a water droplet. Thus, when white light hits the water droplet (assume spherical) the angles at which each color emerges is different. Again, this is due to the fact that each color has different indices of refraction, for example blue will refract more than red. Red light emerges at about 42° and blue light emgerges at about 40.5° with respect to the incoming ray of light. If we recall the fact that we only see the Descartes ray from a single drop we can conclude that each water droplet contributes to only one color of the rainbow.

Since each raindrop produces only one color, a rainbow must consist of many raindrops. In fact, the raindrops lower in the sky contributes to the blue light, and the drops higher in the sky contributes red light. This is because we see red light at about 42° to our eye and blue light at about 40.5° to our eye. Simple geometry then shows that the blue droplet must be lower. So to see a rainbow of colors red, orange, yellow, green, blue, and violet, the red light must be seen from a droplet higher than the droplet for the other colors, and the violet light must be seen from a droplet lower than the rest. Thus when we see a rainbow we see red on the top of the arc and violet on the bottom respectively.

On occasions we see a secondary rainbow which is

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