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Simple question: Water is clearly not disspersive if we have it, for example, in a glass of water. We don't see the rainbow through a glass of water. However drops of water disperse light in the atmosphere and allow us to see the rainbow, am I right? Why is this? In which conditions is water disspersive and in which conditions it's not?.

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  • $\begingroup$ I see rainbows in glasses of water! A narrow beam of reflected sunlight passing through the glass about half way between the center and edge will do the trick. $\endgroup$ – uhoh Jun 3 '17 at 16:51
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The dispersion that leads to the rainbow effect generated by transparent media results from an intrinsic property of the medium being considered: the dependence of its refractive index $n$ on the wavelength of light $\lambda$ passing through it. In this sense, water in a glass is just as dispersive as water droplets in a rainbow.

When different wavelengths pass from air into a sample of water, they refract by different amounts according to Snell's law, and the fact that the index of refraction of water varies as a function of wavelength.

So why don't you see a rainbow in some situations, but you do see a rainbow in others? Well, it's because being able to see the rainbow depends on the geometry of the sample of water, at what angle the light is incident, and where the dispersed light is being viewed from.

For example, suppose we have a sample of white light (containing all wavelengths) that is normally (perpendicular to the surface) incident on a rectangular prism of water, then by Snell's law, the the light does not refract at all when it passes through the sample, and we see no dispersion.

On the other hand, if there is a droplet on a table, then we can arrange for white light to be shone on the droplet in such a way that it is not normally incident on the droplet and exits the droplet in such a way that it hits the table allowing us to see all of the separated colors.

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  • $\begingroup$ So if I incide light not normally in a big amount of water, will I see dispersion? Shouldn't then I see dispersion by looking at the sun (when it's NOT on top of the sky) from behind the water, for example in the sea? $\endgroup$ – MyUserIsThis Jul 8 '13 at 21:06
  • $\begingroup$ You don't need to go underwater to see this effect. Just look up at the blue sky $\endgroup$ – Bill Alsept Apr 4 '17 at 21:33

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