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When the wave fronts of light pass through a barrier that has many slits, different wavelengths appear at different angles. What I don't understand is that why is it when the angle changes so does the wavelength (the color) of light,,?

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The light waves from the many slits overlaps and you see the result of that overlapping. Along certain directions (at certain angles) the waves of a particular wavelength from all of the slits overlap in such a way so as to reinforce one another to produce light of high intensity. That direction depends on the wavelength of the light and so for different angles you see light of different colours (wavelengths).

The device is called a diffraction grating and there is a formula which predicts the directions of high intensity.

$n \lambda = d \sin \theta$

where $n$ is an integer, $\lambda$ is the wavelength of the light, $d$ is the separation of he slits and $\theta$ is the angle.

Later
Here is a highly stylised diagram of what might happen to white light which is made up of many wavelengths

enter image description here

Note that the same effect can be obtained from a whole lot of reflecting surfaces as there are on a CD or DVD.

enter image description here

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  • $\begingroup$ Thank you, but do waves of different wavelengths overlap too or just those the same? And how do slits separate the wavelengths of light? $\endgroup$ – user65035 Feb 5 '16 at 10:44
  • $\begingroup$ I have added to my answer above. $\endgroup$ – Farcher Feb 5 '16 at 12:40

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