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Can we produce a white laser from a visible light spectrum?

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I am doing a final year project, my Prof gave me 2 prism.
He wants me to do so:
A white laser is shot on a prism producing a visible light spectrum, use another prism to converge the spectrum back into a laser.

For me, it is theoretically impossible and I tried to convince him that it doesn't work as prism can only make the light more disperse. But he insisted that by principle of reversibility, there should be a way to convert the spectrum back to a laser.

Is he really correct? I want to disprove his statement but I cannot figure out a concrete proof.

I don't know what to do now.

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