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my question might be quite simple for some of you but I don't have any idea what the result of such an experiment would be...

If you would take an image emitting light such as a video from a screen and would pass that white light through a prism and then pass these color spectrum waves through another prism, would it recombine the initial white light beam and see the exact same image\video that was emitted from the screen?

If it is not possible, is there a way the color spectrum waves could be recombined into the initial picture?

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Yes it is possible to see the exact video after successive dispersions. Although the final image or video might be diminished in intensity because of absorption by the prism. At first the white light splits into seperate portions of the electromagnetic spectrum(like visible,UV,IR etc.) and then these spectra recombine smmothly to form the white light after the next dispersion. If you wanna learn more here is a useful link:

https://en.m.wikipedia.org/wiki/Dispersion_(optics)

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