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Does light change its color after diffraction? lets have example of red light that is passing through garting, after passing it ,doest it change its color after diffraction?

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Diffraction occurs when a wave passes an edge, passes through a narrow gap or goes past an object. None of the properties of a wave are changed by diffraction. The wavelength, frequency, period and speed are same before and after diffraction. Again, the only change is the direction in which the wave is travelling.

As wavelength does not change, the colour of light never changes.

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A diffraction grating does not affect the color of light that is diffracted by the grating. If a single-wavelength light beam enters the grating, only that same wavelength exits the grating. Adding the complication of having a medium of one refractive index on one side of the grating and a different refractive index on the other side does not change anything important. The wavelength shift that light experiences in going from one medium to another does not affect the energy of the photons. If the light struck the color-sensitive receptors in your eye, or any other color-sensitive detector, there would be no photon energy difference detectable and therefore no color difference.

There is one exception: if the diffraction grating is moving, it will shift the energy of the photons - and their wavelengths - and their detectable color. The same is true of a moving mirror. A prime example is an acousto-optic beam deflector, in which a very high intensity acoustic wave travels through a transparent medium, forming a moving diffraction grating. A light beam passing through the moving diffraction grating is, of course, diffracted. Usually multiple beams emerge from the grating, each beam corresponding to a different diffraction order. Each diffracted beam is frequency-shifted by NxF, where F is the frequency of the acoustic wave and N is the diffraction order of the diffracted beam. The frequency shift is in fact an energy shift: the diffracted photons have a different energy than the incident photons.

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Additional to the given answers only one remark.

Photons are indivisible units. As long as they not get received by an electron of the slits surface it stays unchanged. By this there is a chance that the exited electrons emit photonsof differet wavelength and some of this photons will reach the observation screen. Furthermore the slits material has anyway a thermal radiation and by this some amount of IR photons arrives the screen too.

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It depends on the medium you have after grating. If it's the same as the medium you have before the grating (where the light is coming from, the source), then no, the colour will not change.

Remember that whenever light propogates from one medium to another (a different one!), the only thing that remains the same is its frequency (if the two media are the same, the frequency as well as the speed and wavelength of the light will be the same) because frequency is a property of the source, not the medium.

Now let's suppose you have a denser medium (relative to what was before the grating) after the grating. Since the medium is denser, by definition of a denser medium, the light will slow down after the grating (speed of light in the denser medium will be lesser). I'm assuming you're familiar with the formula $v$ = $\lambda$ $\nu$ (speed=frequency×wavelength). Now as I mentioned before, the frequency has to remain the same. In other words the ratio $v$ ÷ $\lambda$ (speed÷wavelength) = $\nu$ (frequency) has to be a constant. But since the speed is reducing, the wavelength will have to decrease too, to maintain the constancy of the frequency. Hence the wavelength of the light will decrease and it will be shifted towards the blue side.

Similarly if the medium after the grating is rarer (relative to what was before the grating), the light would move towards the red side (till as red as it can get)

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    $\begingroup$ It is not correct that changing the wavelength by passing from one medium to another changes the color of the beam. Color depends on the relative sensitivity of receptors in your eye to the energy of the photons. Although moving between media with different refractive indices shifts the wavelength within the media, it does not change the photon energies. $\endgroup$ – S. McGrew Mar 22 '18 at 8:02

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