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What are the distinct differences, if any, between Coherent Light, Light that is In Phase, and Polarized Light?

Also: I have found conflicting definitions of coherent light, where one definition is "constant phase difference" but another stating the waves must be all in-phase. I've attached two photos. The first photo shows that two waves are in phase as long as phase difference is constant. The second photo indicates that the waves must be in-phase in order for them to be coherent. Which is correct?

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Coherence means waves which maintain the same phase difference between them as you mentioned. So the two waves in the first picture are coherent if they maintain the same phase difference. Note that this implies that they must have the same frequency.

Polarized waves are just waves oscillating about one plane. They need not be monochromatic, coherent or in phase.

In phase waves are those which maintain no phase difference between them, so saying in phase implies the waves are coherent.

The 2nd picture says that the waves are in phase so they are also coherent.

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  • $\begingroup$ In the second picture in the second row ("LED: one color...") why does it say the light is not-coherent if it appears that the phase difference between the waves is constant? Since the waves are monochromatic, doesn't this imply they are coherent? $\endgroup$
    – Rickmer
    Commented Mar 4, 2018 at 19:34
  • $\begingroup$ It is not at all obvious just by looking at it that they have the same phase difference. If waves are monochromatic at all they don't have to be coherent. Monochromatic means they are same colour. $\endgroup$
    – SmarthBansal
    Commented Mar 5, 2018 at 12:09

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