Alternating violet and red fringes in Diffraction Grating

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When white light passes through a diffraction grating, it creates various order spectra on a screen. Violet light, due to its shorter wavelength, appears closer to the zeroth order bright fringe than red light, but this only applies to fringes of the same order. In higher orders, such as the first or second, violet fringes can appear beyond red fringes. This means that the 2nd-order violet fringe can be positioned beyond the 1st-order red fringe. The alternating pattern of violet and red lights results from the different orders of the spectra produced by the grating.
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When white light is passed through the slits in the grate and hits a screen some distance away from the grate, different order spectra appear. My textbook tells me that violet light is always closer to the zeroth order bright fringe than red light because it has a shorter wavelength. However, other sources clearly state that the pattern that appears on the screen is of an alternating pattern of violet and red lights, forming different order spectra. So, why would there be violet fringes beyond red fringes even though their wavelengths remain unchanged?
 
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In other words, the 2nd-order violet fringe is beyond the 1st-order red fringe. The statement "violet light is always closer to the zeroth order bright fringe than red light" is only true for a violet and red fringe of the same order; so the 1st-order violet is closer than the 1st-order red, 2nd-order violet is closer than 2nd-order red, etc.
 
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